diff --git a/CHANGELOG.md b/CHANGELOG.md
index 2dcdb3d924..0889f2da79 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -849,6 +849,7 @@ Non-backwards compatible changes
   IO.Effectful
   IO.Instances
   ```
+
 ### (Issue #2096) Introduction of flipped relation symbol for `Relation.Binary.Bundles.Preorder`
 
 * Previously, the relation symbol `_∼_`  was (notationally) symmetric, so that its
@@ -989,6 +990,53 @@ Non-backwards compatible changes
   Relation.Binary.Reasoning.PartialOrder
   ```
 
+### More modular design of equational reasoning.
+
+* Have introduced a new module `Relation.Binary.Reasoning.Syntax` which exports
+  a range of modules containing pre-existing reasoning combinator syntax.
+
+* This makes it possible to add new or rename existing reasoning combinators to a
+  pre-existing `Reasoning` module in just a couple of lines
+  (e.g. see `∣-Reasoning` in `Data.Nat.Divisibility`)
+
+* One pre-requisite for that is that `≡-Reasoning` has been moved from
+  `Relation.Binary.PropositionalEquality.Core` (which shouldn't be
+  imported anyway as it's a `Core` module) to 
+  `Relation.Binary.PropositionalEquality.Properties`.
+  It is still exported by `Relation.Binary.PropositionalEquality`.
+
+### Renaming of symmetric combinators for equational reasoning
+
+* We've had various complaints about the symmetric version of reasoning combinators 
+  that use the syntax `_R˘⟨_⟩_` for some relation `R`, (e.g. `_≡˘⟨_⟩_` and `_≃˘⟨_⟩_`)
+  introduced in `v1.0`. In particular:
+  1. The symbol `˘` is hard to type.
+  2. The symbol `˘` doesn't convey the direction of the equality
+  3. The left brackets aren't vertically aligned with the left brackets of the non-symmetric version.
+  
+* To address these problems we have renamed all the symmetric versions of the 
+  combinators from `_R˘⟨_⟩_` to `_R⟨_⟨_` (the direction of the last bracket is flipped
+  to indicate the quality goes from right to left).
+  
+* The old combinators still exist but have been deprecated. However due to 
+  [Agda issue #5617](https://github.com/agda/agda/issues/5617), the deprecation warnings
+  don't fire correctly. We will not remove the old combinators before the above issue is
+  addressed. However, we still encourage migrating to the new combinators!
+
+* On a Linux-based system, the following command was used to globally migrate all uses of the
+  old combinators to the new ones in the standard library itself. 
+  It *may* be useful when trying to migrate your own code:
+  ```bash
+  find . -type f -name "*.agda" -print0 | xargs -0 sed -i -e 's/˘⟨\(.*\)⟩/⟨\1⟨/g'
+  ```
+  USUAL CAVEATS: It has not been widely tested and the standard library developers are not 
+  responsible for the results of this command. It is strongly recommended you back up your 
+  work before you attempt to run it.
+  
+* NOTE: this refactoring may require some extra bracketing around the operator `_⟨_⟩_` from 
+  `Function.Base` if the `_⟨_⟩_` operator is used within the reasoning proof. The symptom
+  for this is a `Don't know how to parse` error.
+
 ### Other
 
 * In accordance with changes to the flags in Agda 2.6.3, all modules that previously used
@@ -1228,21 +1276,6 @@ Major improvements
   * `RawLattice` has been moved from `Algebra.Lattice.Bundles` to this new module.
 
 * In `Relation.Binary.Reasoning.Base.Triple`, added a new parameter `<-irrefl : Irreflexive _≈_ _<_`
-
-### More modular design of equational reasoning.
-
-* Have introduced a new module `Relation.Binary.Reasoning.Syntax` which exports
-  a range of modules containing pre-existing reasoning combinator syntax.
-
-* This makes it possible to add new or rename existing reasoning combinators to a
-  pre-existing `Reasoning` module in just a couple of lines
-  (e.g. see `∣-Reasoning` in `Data.Nat.Divisibility`)
-
-* One pre-requisite for that is that `≡-Reasoning` has been moved from
-  `Relation.Binary.PropositionalEquality.Core` (which shouldn't be
-  imported anyway as it's a `Core` module) to 
-  `Relation.Binary.PropositionalEquality.Properties`.
-  It is still exported by `Relation.Binary.PropositionalEquality`.
   
 Deprecated modules
 ------------------
diff --git a/README/Data/Fin/Relation/Unary/Top.agda b/README/Data/Fin/Relation/Unary/Top.agda
index e602932827..390a48d58f 100644
--- a/README/Data/Fin/Relation/Unary/Top.agda
+++ b/README/Data/Fin/Relation/Unary/Top.agda
@@ -76,8 +76,8 @@ opposite-prop {suc n} i with view i
 ... | ‵fromℕ  rewrite toℕ-fromℕ n | n∸n≡0 n = refl
 ... | ‵inject₁ j = begin
   suc (toℕ (opposite j)) ≡⟨ cong suc (opposite-prop j) ⟩
-  suc (n ∸ suc (toℕ j))  ≡˘⟨ +-∸-assoc 1 (toℕ<n j) ⟩
-  n ∸ toℕ j              ≡˘⟨ cong (n ∸_) (toℕ-inject₁ j) ⟩
+  suc (n ∸ suc (toℕ j))  ≡⟨ +-∸-assoc 1 (toℕ<n j) ⟨
+  n ∸ toℕ j              ≡⟨ cong (n ∸_) (toℕ-inject₁ j) ⟨
   n ∸ toℕ (inject₁ j)    ∎ where open ≡-Reasoning
 
 ------------------------------------------------------------------------
diff --git a/README/Data/Vec/Relation/Binary/Equality/Cast.agda b/README/Data/Vec/Relation/Binary/Equality/Cast.agda
index fb76544ed7..42cd8bfd3d 100644
--- a/README/Data/Vec/Relation/Binary/Equality/Cast.agda
+++ b/README/Data/Vec/Relation/Binary/Equality/Cast.agda
@@ -86,7 +86,7 @@ example1a-fromList-∷ʳ : ∀ (x : A) xs .(eq : L.length (xs L.∷ʳ x) ≡ suc
                         cast eq (fromList (xs L.∷ʳ x)) ≡ fromList xs ∷ʳ x
 example1a-fromList-∷ʳ x xs eq = begin
   cast eq (fromList (xs L.∷ʳ x))                   ≡⟨⟩
-  cast eq (fromList (xs L.++ L.[ x ]))             ≡˘⟨ cast-trans eq₁ eq₂ (fromList (xs L.++ L.[ x ])) ⟩
+  cast eq (fromList (xs L.++ L.[ x ]))             ≡⟨ cast-trans eq₁ eq₂ (fromList (xs L.++ L.[ x ])) ⟨
   cast eq₂ (cast eq₁ (fromList (xs L.++ L.[ x ]))) ≡⟨ cong (cast eq₂) (fromList-++ xs) ⟩
   cast eq₂ (fromList xs ++ [ x ])                  ≡⟨ ≈-sym (unfold-∷ʳ (sym eq₂) x (fromList xs)) ⟩
   fromList xs ∷ʳ x                                 ∎
@@ -105,7 +105,7 @@ example1b-fromList-∷ʳ : ∀ (x : A) xs .(eq : L.length (xs L.∷ʳ x) ≡ suc
 example1b-fromList-∷ʳ x xs eq = begin
   fromList (xs L.∷ʳ x)       ≈⟨⟩
   fromList (xs L.++ L.[ x ]) ≈⟨ fromList-++ xs ⟩
-  fromList xs ++ [ x ]       ≈˘⟨ unfold-∷ʳ (+-comm 1 (L.length xs)) x (fromList xs) ⟩
+  fromList xs ++ [ x ]       ≈⟨ unfold-∷ʳ (+-comm 1 (L.length xs)) x (fromList xs) ⟨
   fromList xs ∷ʳ x           ∎
   where open CastReasoning
 
@@ -120,10 +120,10 @@ example1b-fromList-∷ʳ x xs eq = begin
 --     ≈-trans     : xs ≈[ m≡n ] ys → ys ≈[ n≡o ] zs → xs ≈[ trans m≡n n≡o ] zs
 -- Accordingly, `_≈[_]_` admits the standard set of equational reasoning
 -- combinators. Suppose `≈-eqn : xs ≈[ m≡n ] ys`,
---     xs ≈⟨ ≈-eqn  ⟩   -- `_≈⟨_⟩_` takes a `_≈[_]_` step, adjusting
---     ys               -- the index at the same time
+--     xs ≈⟨ ≈-eqn ⟩   -- `_≈⟨_⟩_` takes a `_≈[_]_` step, adjusting
+--     ys              -- the index at the same time
 --
---     ys ≈˘⟨ ≈-eqn ⟩   -- `_≈˘⟨_⟩_` takes a symmetric `_≈[_]_` step
+--     ys ≈⟨ ≈-eqn ⟨   -- `_≈⟨_⟨_` takes a symmetric `_≈[_]_` step
 --     xs
 example2a : ∀ .(eq : suc m + n ≡ m + suc n) (xs : Vec A m) a ys →
             cast eq ((reverse xs ∷ʳ a) ++ ys) ≡ reverse xs ++ (a ∷ ys)
@@ -138,7 +138,7 @@ example2a eq xs a ys = begin
 --     xs ≂⟨ ≡-eqn  ⟩    -- Takes a `_≡_` step; no change to the index
 --     ys
 --
---     ys ≂˘⟨ ≡-eqn ⟩    -- Takes a symmetric `_≡_` step
+--     ys ≂⟨ ≡-eqn ⟨    -- Takes a symmetric `_≡_` step
 --     xs
 -- Equivalently, `≈-reflexive` injects `_≡_` into `_≈[_]_`. That is,
 -- `xs ≂⟨ ≡-eqn ⟩ ys` is the same as `xs ≈⟨ ≈-reflexive ≡-eqn ⟩ ys`.
@@ -149,7 +149,7 @@ example2b eq xs a ys = begin
   (a ∷ xs) ʳ++ ys         ≂⟨ unfold-ʳ++ (a ∷ xs) ys ⟩          -- index: suc m + n
   reverse (a ∷ xs) ++ ys  ≂⟨ cong (_++ ys) (reverse-∷ a xs) ⟩  -- index: suc m + n
   (reverse xs ∷ʳ a) ++ ys ≈⟨ ∷ʳ-++ eq a (reverse xs) ⟩         -- index: suc m + n
-  reverse xs ++ (a ∷ ys)  ≂˘⟨ unfold-ʳ++ xs (a ∷ ys) ⟩         -- index: m + suc n
+  reverse xs ++ (a ∷ ys)  ≂⟨ unfold-ʳ++ xs (a ∷ ys) ⟨         -- index: m + suc n
   xs ʳ++ (a ∷ ys)         ∎                                    -- index: m + suc n
   where open CastReasoning
 
@@ -201,11 +201,11 @@ example3b-fromList-++-++′ {xs = xs} {ys} {zs} eq = begin
 example4-cong² : ∀ .(eq : (m + 1) + n ≡ n + suc m) a (xs : Vec A m) ys →
           cast eq (reverse ((xs ++ [ a ]) ++ ys)) ≡ ys ʳ++ reverse (xs ∷ʳ a)
 example4-cong² {m = m} {n} eq a xs ys = begin
-  reverse ((xs ++ [ a ]) ++ ys)   ≈˘⟨ ≈-cong reverse (cast-reverse (cong (_+ n) (+-comm 1 m)) ((xs ∷ʳ a) ++ ys))
+  reverse ((xs ++ [ a ]) ++ ys)   ≈⟨ ≈-cong reverse (cast-reverse (cong (_+ n) (+-comm 1 m)) ((xs ∷ʳ a) ++ ys))
                                              (≈-cong (_++ ys) (cast-++ˡ (+-comm 1 m) (xs ∷ʳ a))
-                                                     (unfold-∷ʳ _ a xs)) ⟩
+                                                     (unfold-∷ʳ _ a xs)) ⟨
   reverse ((xs ∷ʳ a) ++ ys)       ≈⟨ reverse-++ (+-comm (suc m) n) (xs ∷ʳ a) ys ⟩
-  reverse ys ++ reverse (xs ∷ʳ a) ≂˘⟨ unfold-ʳ++ ys (reverse (xs ∷ʳ a)) ⟩
+  reverse ys ++ reverse (xs ∷ʳ a) ≂⟨ unfold-ʳ++ ys (reverse (xs ∷ʳ a)) ⟨
   ys ʳ++ reverse (xs ∷ʳ a)        ∎
   where open CastReasoning
 
@@ -237,7 +237,7 @@ example5-fromList-++-++′ {xs = xs} {ys} {zs} eq = begin
 -- and then switch to the reasoning system of `_≈[_]_`.
 example6a-reverse-∷ʳ : ∀ x (xs : Vec A n) → reverse (xs ∷ʳ x) ≡ x ∷ reverse xs
 example6a-reverse-∷ʳ {n = n} x xs = begin-≡
-  reverse (xs ∷ʳ x)     ≡˘⟨ ≈-reflexive refl ⟩
+  reverse (xs ∷ʳ x)     ≡⟨ ≈-reflexive refl ⟨
   reverse (xs ∷ʳ x)     ≈⟨ ≈-cong reverse (cast-reverse _ _) (unfold-∷ʳ (+-comm 1 n) x xs) ⟩
   reverse (xs ++ [ x ]) ≈⟨ reverse-++ (+-comm n 1) xs [ x ] ⟩
   x ∷ reverse xs        ∎
@@ -249,6 +249,6 @@ example6b-reverse-∷ʳ-by-induction x (y ∷ xs) = begin
   reverse (y ∷ (xs ∷ʳ x)) ≡⟨ reverse-∷ y (xs ∷ʳ x) ⟩
   reverse (xs ∷ʳ x) ∷ʳ y  ≡⟨ cong (_∷ʳ y) (example6b-reverse-∷ʳ-by-induction x xs) ⟩
   (x ∷ reverse xs) ∷ʳ y   ≡⟨⟩
-  x ∷ (reverse xs ∷ʳ y)   ≡˘⟨ cong (x ∷_) (reverse-∷ y xs) ⟩
+  x ∷ (reverse xs ∷ʳ y)   ≡⟨ cong (x ∷_) (reverse-∷ y xs) ⟨
   x ∷ reverse (y ∷ xs)    ∎
   where open ≡-Reasoning
diff --git a/README/Tactic/Cong.agda b/README/Tactic/Cong.agda
index 6503604d71..20cb5ad7d9 100644
--- a/README/Tactic/Cong.agda
+++ b/README/Tactic/Cong.agda
@@ -33,7 +33,7 @@ verbose-example m n eq =
     suc (suc m) + m
   ≡⟨ cong (λ ϕ → suc (suc (ϕ + ϕ))) eq ⟩
     suc (suc n) + n
-  ≡˘⟨ cong (λ ϕ → suc (suc (n + ϕ))) (+-identityʳ n) ⟩
+  ≡⟨ cong (λ ϕ → suc (suc (n + ϕ))) (+-identityʳ n) ⟨
     suc (suc n) + (n + 0)
   ∎
 
@@ -51,7 +51,7 @@ succinct-example m n eq =
     suc (suc m) + m
   ≡⟨ cong! eq ⟩
     suc (suc n) + n
-  ≡˘⟨ cong! (+-identityʳ n) ⟩
+  ≡⟨ cong! (+-identityʳ n) ⟨
     suc (suc n) + (n + 0)
   ∎
 
@@ -124,7 +124,7 @@ module EquationalReasoningTests where
       suc (suc m) + m
     ≡⟨ cong! eq ⟩
       suc (suc n) + n
-    ≡˘⟨ cong! (+-identityʳ n) ⟩
+    ≡⟨ cong! (+-identityʳ n) ⟨
       suc (suc n) + (n + 0)
     ∎
 
diff --git a/src/Algebra/Apartness/Properties/HeytingCommutativeRing.agda b/src/Algebra/Apartness/Properties/HeytingCommutativeRing.agda
index 7f4f164f42..868224bf0c 100644
--- a/src/Algebra/Apartness/Properties/HeytingCommutativeRing.agda
+++ b/src/Algebra/Apartness/Properties/HeytingCommutativeRing.agda
@@ -56,11 +56,11 @@ x#0y#0→xy#0 {x} {y} x#0 y#0 = helper (#⇒invertible x#0) (#⇒invertible y#0)
     y⁻¹*x⁻¹*x*y≈1 = begin
       y⁻¹ * x⁻¹ * (x * y - 0#)     ≈⟨ *-congˡ (x-0≈x (x * y)) ⟩
       y⁻¹ * x⁻¹ * (x * y)          ≈⟨ *-assoc y⁻¹ x⁻¹ (x * y) ⟩
-      y⁻¹ * (x⁻¹ * (x * y))       ≈˘⟨ *-congˡ (*-assoc x⁻¹ x y) ⟩
-      y⁻¹ * ((x⁻¹ * x) * y)       ≈˘⟨ *-congˡ (*-congʳ (*-congˡ (x-0≈x x))) ⟩
+      y⁻¹ * (x⁻¹ * (x * y))       ≈⟨ *-congˡ (*-assoc x⁻¹ x y) ⟨
+      y⁻¹ * ((x⁻¹ * x) * y)       ≈⟨ *-congˡ (*-congʳ (*-congˡ (x-0≈x x))) ⟨
       y⁻¹ * ((x⁻¹ * (x - 0#)) * y) ≈⟨ *-congˡ (*-congʳ x⁻¹*x≈1) ⟩
       y⁻¹ * (1# * y)               ≈⟨ *-congˡ (*-identityˡ y) ⟩
-      y⁻¹ * y                     ≈˘⟨ *-congˡ (x-0≈x y) ⟩
+      y⁻¹ * y                     ≈⟨ *-congˡ (x-0≈x y) ⟨
       y⁻¹ * (y - 0#)               ≈⟨ y⁻¹*y≈1 ⟩
       1# ∎
 
@@ -75,15 +75,15 @@ x#0y#0→xy#0 {x} {y} x#0 y#0 = helper (#⇒invertible x#0) (#⇒invertible y#0)
 
   y-x≈-[x-y] : y - x ≈ - (x - y)
   y-x≈-[x-y] = begin
-    y - x     ≈˘⟨ +-congʳ (-‿involutive y) ⟩
-    - - y - x ≈˘⟨ -‿anti-homo-+ x (- y) ⟩
+    y - x     ≈⟨ +-congʳ (-‿involutive y) ⟨
+    - - y - x ≈⟨ -‿anti-homo-+ x (- y) ⟨
     - (x - y) ∎
 
   x-y⁻¹*y-x≈1 : (- x-y⁻¹) * (y - x) ≈ 1#
   x-y⁻¹*y-x≈1 = begin
-    (- x-y⁻¹) * (y - x)   ≈˘⟨ -‿distribˡ-* x-y⁻¹ (y - x) ⟩
+    (- x-y⁻¹) * (y - x)   ≈⟨ -‿distribˡ-* x-y⁻¹ (y - x) ⟨
     - (x-y⁻¹ * (y - x))    ≈⟨ -‿cong (*-congˡ y-x≈-[x-y]) ⟩
-    - (x-y⁻¹ * - (x - y)) ≈˘⟨ -‿cong (-‿distribʳ-* x-y⁻¹ (x - y)) ⟩
+    - (x-y⁻¹ * - (x - y)) ≈⟨ -‿cong (-‿distribʳ-* x-y⁻¹ (x - y)) ⟨
     - - (x-y⁻¹ * (x - y))  ≈⟨ -‿involutive (x-y⁻¹ * ((x - y))) ⟩
     x-y⁻¹ * (x - y)        ≈⟨ InvX-Y .proj₂ .proj₁ ⟩
     1# ∎
@@ -100,7 +100,7 @@ x#0y#0→xy#0 {x} {y} x#0 y#0 = helper (#⇒invertible x#0) (#⇒invertible y#0)
 
     x-z⁻¹*y-z≈1 : x-z⁻¹ * (y - z) ≈ 1#
     x-z⁻¹*y-z≈1 = begin
-      x-z⁻¹ * (y - z) ≈˘⟨ *-congˡ (+-congʳ x≈y) ⟩
+      x-z⁻¹ * (y - z) ≈⟨ *-congˡ (+-congʳ x≈y) ⟨
       x-z⁻¹ * (x - z)  ≈⟨ x-z⁻¹*x-z≈1# ⟩
       1# ∎
 
diff --git a/src/Algebra/Consequences/Setoid.agda b/src/Algebra/Consequences/Setoid.agda
index 1aa2b8f4c8..068ecb2d12 100644
--- a/src/Algebra/Consequences/Setoid.agda
+++ b/src/Algebra/Consequences/Setoid.agda
@@ -88,7 +88,7 @@ module _ {f : Op₁ A} (self : SelfInverse f) where
 
   selfInverse⇒injective : Injective _≈_ _≈_ f
   selfInverse⇒injective {x} {y} x≈y = begin
-    x       ≈˘⟨ self x≈y ⟩
+    x       ≈⟨ self x≈y ⟨
     f (f y) ≈⟨ selfInverse⇒involutive y ⟩
     y       ∎
 
@@ -267,12 +267,12 @@ module _ {_•_ _◦_ : Op₂ A}
                              _◦_ DistributesOver _•_ →
                              _•_ DistributesOverˡ _◦_
   distrib+absorbs⇒distribˡ •-absorbs-◦ ◦-absorbs-• (◦-distribˡ-• , ◦-distribʳ-•) x y z = begin
-    x • (y ◦ z)                    ≈˘⟨ •-cong (•-absorbs-◦ _ _) refl ⟩
+    x • (y ◦ z)                    ≈⟨ •-cong (•-absorbs-◦ _ _) refl ⟨
     (x • (x ◦ y)) • (y ◦ z)        ≈⟨  •-cong (•-cong refl (◦-comm _ _)) refl ⟩
     (x • (y ◦ x)) • (y ◦ z)        ≈⟨  •-assoc _ _ _ ⟩
-    x • ((y ◦ x) • (y ◦ z))        ≈˘⟨ •-cong refl (◦-distribˡ-• _ _ _) ⟩
-    x • (y ◦ (x • z))              ≈˘⟨ •-cong (◦-absorbs-• _ _) refl ⟩
-    (x ◦ (x • z)) • (y ◦ (x • z))  ≈˘⟨ ◦-distribʳ-• _ _ _ ⟩
+    x • ((y ◦ x) • (y ◦ z))        ≈⟨ •-cong refl (◦-distribˡ-• _ _ _) ⟨
+    x • (y ◦ (x • z))              ≈⟨ •-cong (◦-absorbs-• _ _) refl ⟨
+    (x ◦ (x • z)) • (y ◦ (x • z))  ≈⟨ ◦-distribʳ-• _ _ _ ⟨
     (x • y) ◦ (x • z)              ∎
 
 ------------------------------------------------------------------------
diff --git a/src/Algebra/Construct/LexProduct/Inner.agda b/src/Algebra/Construct/LexProduct/Inner.agda
index 9b6e06f0e6..beff9e9e3a 100644
--- a/src/Algebra/Construct/LexProduct/Inner.agda
+++ b/src/Algebra/Construct/LexProduct/Inner.agda
@@ -82,8 +82,8 @@ module NaturalOrder where
 
   ≤∙ˡ-trans : Associative _≈₁_ _∙_ → (a ∙ b) ≈₁ b → (b ∙ c) ≈₁ c → (a ∙ c) ≈₁ c
   ≤∙ˡ-trans {a} {b} {c} ∙-assoc ab≈b bc≈c = begin
-    a ∙ c        ≈˘⟨ ∙-congˡ bc≈c ⟩
-    a ∙ (b ∙ c)  ≈˘⟨ ∙-assoc a b c ⟩
+    a ∙ c        ≈⟨ ∙-congˡ bc≈c ⟨
+    a ∙ (b ∙ c)  ≈⟨ ∙-assoc a b c ⟨
     (a ∙ b) ∙ c  ≈⟨  ∙-congʳ ab≈b ⟩
     b ∙ c        ≈⟨  bc≈c ⟩
     c            ∎
@@ -179,51 +179,51 @@ assoc ∙-assoc ∙-comm ∙-sel ◦-assoc a b c x y z
 ... | no ab≉a  | yes ab≈b | yes bc≈b | yes bc≈c = begin
   lex (a ∙ b) c y z        ≈⟨  cong₁ ab≈b ⟩
   lex b c y z              ≈⟨  case₃ bc≈b bc≈c ⟩
-  y ◦ z                    ≈˘⟨ case₂ ab≉a ab≈b ⟩
-  lex a b x (y ◦ z)        ≈˘⟨ cong₂ bc≈b ⟩
+  y ◦ z                    ≈⟨ case₂ ab≉a ab≈b ⟨
+  lex a b x (y ◦ z)        ≈⟨ cong₂ bc≈b ⟨
   lex a (b ∙ c) x (y ◦ z)  ∎
 ... | no ab≉a  | yes ab≈b | yes bc≈b | no bc≉c = begin
   lex (a ∙ b) c y z        ≈⟨  cong₁ ab≈b ⟩
   lex b c y z              ≈⟨  case₁ bc≈b bc≉c ⟩
-  y                        ≈˘⟨ case₂ ab≉a ab≈b ⟩
-  lex a b x y              ≈˘⟨ cong₂ bc≈b ⟩
+  y                        ≈⟨ case₂ ab≉a ab≈b ⟨
+  lex a b x y              ≈⟨ cong₂ bc≈b ⟨
   lex a (b ∙ c) x y        ∎
 ... | yes ab≈a | yes ab≈b | yes bc≈b | no bc≉c = begin
   lex (a ∙ b) c (x ◦ y) z  ≈⟨  cong₁ ab≈b ⟩
   lex b c (x ◦ y) z        ≈⟨  case₁ bc≈b bc≉c ⟩
-  x ◦ y                    ≈˘⟨ case₃ ab≈a ab≈b ⟩
-  lex a b x y              ≈˘⟨ cong₂ bc≈b ⟩
+  x ◦ y                    ≈⟨ case₃ ab≈a ab≈b ⟨
+  lex a b x y              ≈⟨ cong₂ bc≈b ⟨
   lex a (b ∙ c) x y        ∎
 ... | yes ab≈a | yes ab≈b | yes bc≈b | yes bc≈c = begin
   lex (a ∙ b) c (x ◦ y) z  ≈⟨  cong₁ ab≈b ⟩
   lex b c (x ◦ y) z        ≈⟨  case₃ bc≈b bc≈c  ⟩
   (x ◦ y) ◦ z              ≈⟨  ◦-assoc x y z ⟩
-  x ◦ (y ◦ z)              ≈˘⟨ case₃ ab≈a ab≈b ⟩
-  lex a b x (y ◦ z)        ≈˘⟨ cong₂ bc≈b ⟩
+  x ◦ (y ◦ z)              ≈⟨ case₃ ab≈a ab≈b ⟨
+  lex a b x (y ◦ z)        ≈⟨ cong₂ bc≈b ⟨
   lex a (b ∙ c) x (y ◦ z)  ∎
 ... | yes ab≈a | yes ab≈b | no bc≉b | yes bc≈c = begin
   lex (a ∙ b) c (x ◦ y) z  ≈⟨  cong₁ ab≈b ⟩
   lex b c (x ◦ y) z        ≈⟨  case₂ bc≉b bc≈c ⟩
-  z                        ≈˘⟨ case₂ bc≉b bc≈c ⟩
-  lex b c x z              ≈˘⟨ cong₁₂ (M.trans (M.sym ab≈a) ab≈b) bc≈c ⟩
+  z                        ≈⟨ case₂ bc≉b bc≈c ⟨
+  lex b c x z              ≈⟨ cong₁₂ (M.trans (M.sym ab≈a) ab≈b) bc≈c ⟨
   lex a (b ∙ c) x z        ∎
 ... | yes ab≈a | no ab≉b | yes bc≈b | yes bc≈c = begin
   lex (a ∙ b) c x z        ≈⟨  cong₁₂ ab≈a (M.trans (M.sym bc≈c) bc≈b) ⟩
   lex a b x z              ≈⟨  case₁ ab≈a ab≉b ⟩
-  x                        ≈˘⟨ case₁ ab≈a ab≉b ⟩
-  lex a b x (y ◦ z)        ≈˘⟨ cong₂ bc≈b ⟩
+  x                        ≈⟨ case₁ ab≈a ab≉b ⟨
+  lex a b x (y ◦ z)        ≈⟨ cong₂ bc≈b ⟨
   lex a (b ∙ c) x (y ◦ z)  ∎
 ... | no ab≉a | yes ab≈b | no bc≉b | yes bc≈c = begin
   lex (a ∙ b) c y z        ≈⟨  cong₁ ab≈b ⟩
   lex b c y z              ≈⟨  case₂ bc≉b bc≈c ⟩
-  z                        ≈˘⟨ uncurry′ case₂ (<∙ˡ-trans ∙-assoc ∙-comm ab≈b ab≉a bc≈c) ⟩
-  lex a c x z              ≈˘⟨ cong₂ bc≈c ⟩
+  z                        ≈⟨ uncurry′ case₂ (<∙ˡ-trans ∙-assoc ∙-comm ab≈b ab≉a bc≈c) ⟨
+  lex a c x z              ≈⟨ cong₂ bc≈c ⟨
   lex a (b ∙ c) x z        ∎
 ... | yes ab≈a | no ab≉b | yes bc≈b | no bc≉c = begin
   lex (a ∙ b) c x z        ≈⟨  cong₁ ab≈a ⟩
   lex a c x z              ≈⟨  uncurry′ case₁ (<∙ʳ-trans ∙-assoc ∙-comm ab≈a bc≈b bc≉c) ⟩
-  x                        ≈˘⟨ case₁ ab≈a ab≉b ⟩
-  lex a b x y              ≈˘⟨ cong₂ bc≈b ⟩
+  x                        ≈⟨ case₁ ab≈a ab≉b ⟨
+  lex a b x y              ≈⟨ cong₂ bc≈b ⟨
   lex a (b ∙ c) x y        ∎
 
 comm : Commutative _≈₁_ _∙_ → Commutative _≈₂_ _◦_ →
diff --git a/src/Algebra/Construct/LiftedChoice.agda b/src/Algebra/Construct/LiftedChoice.agda
index 2433c87b9d..f53eecc7f1 100644
--- a/src/Algebra/Construct/LiftedChoice.agda
+++ b/src/Algebra/Construct/LiftedChoice.agda
@@ -100,8 +100,8 @@ module _ {_≈_ : Rel B ℓ} {_∙_ : Op₂ B}
 
     assoc : Associative _≈_ _∙_ → Associative _≈′_ _◦_
     assoc ∙-assoc x y z = f-injective (begin
-      f ((x ◦ y) ◦ z)   ≈˘⟨ distrib f (x ◦ y) z ⟩
-      f (x ◦ y) ∙ f z   ≈˘⟨ ∙-congʳ (distrib f x y) ⟩
+      f ((x ◦ y) ◦ z)   ≈⟨ distrib f (x ◦ y) z ⟨
+      f (x ◦ y) ∙ f z   ≈⟨ ∙-congʳ (distrib f x y) ⟨
       (f x ∙ f y) ∙ f z ≈⟨  ∙-assoc (f x) (f y) (f z) ⟩
       f x ∙ (f y ∙ f z) ≈⟨  ∙-congˡ (distrib f y z) ⟩
       f x ∙ f (y ◦ z)   ≈⟨  distrib f x (y ◦ z) ⟩
@@ -109,7 +109,7 @@ module _ {_≈_ : Rel B ℓ} {_∙_ : Op₂ B}
 
     comm : Commutative _≈_ _∙_ → Commutative _≈′_ _◦_
     comm ∙-comm x y = f-injective (begin
-      f (x ◦ y) ≈˘⟨ distrib f x y ⟩
+      f (x ◦ y) ≈⟨ distrib f x y ⟨
       f x ∙ f y ≈⟨  ∙-comm (f x) (f y) ⟩
       f y ∙ f x ≈⟨  distrib f y x ⟩
       f (y ◦ x) ∎)
diff --git a/src/Algebra/Construct/NaturalChoice/MinMaxOp.agda b/src/Algebra/Construct/NaturalChoice/MinMaxOp.agda
index 04866f0ad0..7b64727832 100644
--- a/src/Algebra/Construct/NaturalChoice/MinMaxOp.agda
+++ b/src/Algebra/Construct/NaturalChoice/MinMaxOp.agda
@@ -51,11 +51,11 @@ open import Algebra.Construct.NaturalChoice.MaxOp maxOp public
 ⊓-distribˡ-⊔ x y z with total y z
 ... | inj₁ y≤z = begin-equality
   x ⊓ (y ⊔ z)       ≈⟨  ⊓-congˡ x (x≤y⇒x⊔y≈y y≤z) ⟩
-  x ⊓ z             ≈˘⟨ x≤y⇒x⊔y≈y (⊓-monoʳ-≤ x y≤z) ⟩
+  x ⊓ z             ≈⟨ x≤y⇒x⊔y≈y (⊓-monoʳ-≤ x y≤z) ⟨
   (x ⊓ y) ⊔ (x ⊓ z) ∎
 ... | inj₂ y≥z = begin-equality
   x ⊓ (y ⊔ z)       ≈⟨  ⊓-congˡ x (x≥y⇒x⊔y≈x y≥z) ⟩
-  x ⊓ y             ≈˘⟨ x≥y⇒x⊔y≈x (⊓-monoʳ-≤ x y≥z) ⟩
+  x ⊓ y             ≈⟨ x≥y⇒x⊔y≈x (⊓-monoʳ-≤ x y≥z) ⟨
   (x ⊓ y) ⊔ (x ⊓ z) ∎
 
 ⊓-distribʳ-⊔ : _⊓_ DistributesOverʳ _⊔_
@@ -68,11 +68,11 @@ open import Algebra.Construct.NaturalChoice.MaxOp maxOp public
 ⊔-distribˡ-⊓ x y z with total y z
 ... | inj₁ y≤z = begin-equality
   x ⊔ (y ⊓ z)       ≈⟨  ⊔-congˡ x (x≤y⇒x⊓y≈x y≤z) ⟩
-  x ⊔ y             ≈˘⟨ x≤y⇒x⊓y≈x (⊔-monoʳ-≤ x y≤z) ⟩
+  x ⊔ y             ≈⟨ x≤y⇒x⊓y≈x (⊔-monoʳ-≤ x y≤z) ⟨
   (x ⊔ y) ⊓ (x ⊔ z) ∎
 ... | inj₂ y≥z = begin-equality
   x ⊔ (y ⊓ z)       ≈⟨  ⊔-congˡ x (x≥y⇒x⊓y≈y y≥z) ⟩
-  x ⊔ z             ≈˘⟨ x≥y⇒x⊓y≈y (⊔-monoʳ-≤ x y≥z) ⟩
+  x ⊔ z             ≈⟨ x≥y⇒x⊓y≈y (⊔-monoʳ-≤ x y≥z) ⟨
   (x ⊔ y) ⊓ (x ⊔ z) ∎
 
 ⊔-distribʳ-⊓ : _⊔_ DistributesOverʳ _⊓_
@@ -119,11 +119,11 @@ antimono-≤-distrib-⊓ : ∀ {f} → f Preserves _≈_ ⟶ _≈_ → f Preserv
 antimono-≤-distrib-⊓ {f} cong antimono x y with total x y
 ... | inj₁ x≤y = begin-equality
   f (x ⊓ y)  ≈⟨ cong (x≤y⇒x⊓y≈x x≤y) ⟩
-  f x        ≈˘⟨ x≥y⇒x⊔y≈x (antimono x≤y) ⟩
+  f x        ≈⟨ x≥y⇒x⊔y≈x (antimono x≤y) ⟨
   f x ⊔ f y  ∎
 ... | inj₂ y≤x = begin-equality
   f (x ⊓ y)  ≈⟨ cong (x≥y⇒x⊓y≈y y≤x) ⟩
-  f y        ≈˘⟨ x≤y⇒x⊔y≈y (antimono y≤x) ⟩
+  f y        ≈⟨ x≤y⇒x⊔y≈y (antimono y≤x) ⟨
   f x ⊔ f y  ∎
 
 antimono-≤-distrib-⊔ : ∀ {f} → f Preserves _≈_ ⟶ _≈_ → f Preserves _≤_ ⟶ _≥_ →
@@ -131,11 +131,11 @@ antimono-≤-distrib-⊔ : ∀ {f} → f Preserves _≈_ ⟶ _≈_ → f Preserv
 antimono-≤-distrib-⊔ {f} cong antimono x y with total x y
 ... | inj₁ x≤y = begin-equality
   f (x ⊔ y)  ≈⟨ cong (x≤y⇒x⊔y≈y x≤y) ⟩
-  f y        ≈˘⟨ x≥y⇒x⊓y≈y (antimono x≤y) ⟩
+  f y        ≈⟨ x≥y⇒x⊓y≈y (antimono x≤y) ⟨
   f x ⊓ f y  ∎
 ... | inj₂ y≤x = begin-equality
   f (x ⊔ y)  ≈⟨ cong (x≥y⇒x⊔y≈x y≤x) ⟩
-  f x        ≈˘⟨ x≤y⇒x⊓y≈x (antimono y≤x) ⟩
+  f x        ≈⟨ x≤y⇒x⊓y≈x (antimono y≤x) ⟨
   f x ⊓ f y  ∎
 
 x⊓y≤x⊔y : ∀ x y → x ⊓ y ≤ x ⊔ y
diff --git a/src/Algebra/Construct/NaturalChoice/MinOp.agda b/src/Algebra/Construct/NaturalChoice/MinOp.agda
index 744d32e1fe..22d0686f8f 100644
--- a/src/Algebra/Construct/NaturalChoice/MinOp.agda
+++ b/src/Algebra/Construct/NaturalChoice/MinOp.agda
@@ -59,17 +59,17 @@ x⊓y≤y x y with total x y
 ⊓-congˡ x {y} {r} y≈r with total x y
 ... | inj₁ x≤y = begin-equality
   x ⊓ y  ≈⟨  x≤y⇒x⊓y≈x x≤y ⟩
-  x      ≈˘⟨ x≤y⇒x⊓y≈x (≤-respʳ-≈ y≈r x≤y) ⟩
+  x      ≈⟨ x≤y⇒x⊓y≈x (≤-respʳ-≈ y≈r x≤y) ⟨
   x ⊓ r  ∎
 ... | inj₂ y≤x = begin-equality
   x ⊓ y  ≈⟨  x≥y⇒x⊓y≈y y≤x ⟩
   y      ≈⟨  y≈r ⟩
-  r      ≈˘⟨ x≥y⇒x⊓y≈y (≤-respˡ-≈ y≈r y≤x) ⟩
+  r      ≈⟨ x≥y⇒x⊓y≈y (≤-respˡ-≈ y≈r y≤x) ⟨
   x ⊓ r  ∎
 
 ⊓-congʳ : ∀ x → Congruent₁ (_⊓ x)
 ⊓-congʳ x {y₁} {y₂} y₁≈y₂ = begin-equality
-  y₁ ⊓ x  ≈˘⟨ ⊓-comm x y₁ ⟩
+  y₁ ⊓ x  ≈⟨ ⊓-comm x y₁ ⟨
   x  ⊓ y₁ ≈⟨  ⊓-congˡ x y₁≈y₂ ⟩
   x  ⊓ y₂ ≈⟨  ⊓-comm x y₂ ⟩
   y₂ ⊓ x  ∎
@@ -82,16 +82,16 @@ x⊓y≤y x y with total x y
 ⊓-assoc x y r | inj₁ x≤y | inj₁ y≤r = begin-equality
   (x ⊓ y) ⊓ r  ≈⟨ ⊓-congʳ r (x≤y⇒x⊓y≈x x≤y) ⟩
   x ⊓ r        ≈⟨ x≤y⇒x⊓y≈x (trans x≤y y≤r) ⟩
-  x            ≈˘⟨ x≤y⇒x⊓y≈x x≤y ⟩
-  x ⊓ y        ≈˘⟨ ⊓-congˡ x (x≤y⇒x⊓y≈x y≤r) ⟩
+  x            ≈⟨ x≤y⇒x⊓y≈x x≤y ⟨
+  x ⊓ y        ≈⟨ ⊓-congˡ x (x≤y⇒x⊓y≈x y≤r) ⟨
   x ⊓ (y ⊓ r)  ∎
 ⊓-assoc x y r | inj₁ x≤y | inj₂ r≤y = begin-equality
   (x ⊓ y) ⊓ r  ≈⟨ ⊓-congʳ r (x≤y⇒x⊓y≈x x≤y) ⟩
-  x ⊓ r        ≈˘⟨ ⊓-congˡ x (x≥y⇒x⊓y≈y r≤y) ⟩
+  x ⊓ r        ≈⟨ ⊓-congˡ x (x≥y⇒x⊓y≈y r≤y) ⟨
   x ⊓ (y ⊓ r)  ∎
 ⊓-assoc x y r | inj₂ y≤x | _ = begin-equality
   (x ⊓ y) ⊓ r  ≈⟨ ⊓-congʳ r (x≥y⇒x⊓y≈y y≤x) ⟩
-  y ⊓ r        ≈˘⟨ x≥y⇒x⊓y≈y (trans (x⊓y≤x y r) y≤x) ⟩
+  y ⊓ r        ≈⟨ x≥y⇒x⊓y≈y (trans (x⊓y≤x y r) y≤x) ⟨
   x ⊓ (y ⊓ r)  ∎
 
 ⊓-idem : Idempotent _⊓_
@@ -215,11 +215,11 @@ mono-≤-distrib-⊓ : ∀ {f} → f Preserves _≈_ ⟶ _≈_ → f Preserves _
 mono-≤-distrib-⊓ {f} cong mono x y with total x y
 ... | inj₁ x≤y = begin-equality
   f (x ⊓ y)  ≈⟨ cong (x≤y⇒x⊓y≈x x≤y) ⟩
-  f x        ≈˘⟨ x≤y⇒x⊓y≈x (mono x≤y) ⟩
+  f x        ≈⟨ x≤y⇒x⊓y≈x (mono x≤y) ⟨
   f x ⊓ f y  ∎
 ... | inj₂ y≤x = begin-equality
   f (x ⊓ y)  ≈⟨ cong (x≥y⇒x⊓y≈y y≤x) ⟩
-  f y        ≈˘⟨ x≥y⇒x⊓y≈y (mono y≤x) ⟩
+  f y        ≈⟨ x≥y⇒x⊓y≈y (mono y≤x) ⟨
   f x ⊓ f y  ∎
 
 x≤y⇒x⊓z≤y : ∀ {x y} z → x ≤ y → x ⊓ z ≤ y
@@ -250,8 +250,8 @@ x≤y⊓z⇒x≤z y z x≤y⊓z = trans x≤y⊓z (x⊓y≤y y z)
 
 ⊓-triangulate : ∀ x y z → x ⊓ y ⊓ z ≈ (x ⊓ y) ⊓ (y ⊓ z)
 ⊓-triangulate x y z = begin-equality
-  x ⊓ y ⊓ z           ≈˘⟨ ⊓-congʳ z (⊓-congˡ x (⊓-idem y)) ⟩
+  x ⊓ y ⊓ z           ≈⟨ ⊓-congʳ z (⊓-congˡ x (⊓-idem y)) ⟨
   x ⊓ (y ⊓ y) ⊓ z     ≈⟨  ⊓-assoc x _ _ ⟩
   x ⊓ ((y ⊓ y) ⊓ z)   ≈⟨  ⊓-congˡ x (⊓-assoc y y z) ⟩
-  x ⊓ (y ⊓ (y ⊓ z))   ≈˘⟨ ⊓-assoc x y (y ⊓ z) ⟩
+  x ⊓ (y ⊓ (y ⊓ z))   ≈⟨ ⊓-assoc x y (y ⊓ z) ⟨
   (x ⊓ y) ⊓ (y ⊓ z)   ∎
diff --git a/src/Algebra/Lattice/Morphism/LatticeMonomorphism.agda b/src/Algebra/Lattice/Morphism/LatticeMonomorphism.agda
index fe3ceec5be..9eb1d4da24 100644
--- a/src/Algebra/Lattice/Morphism/LatticeMonomorphism.agda
+++ b/src/Algebra/Lattice/Morphism/LatticeMonomorphism.agda
@@ -97,8 +97,8 @@ module _ (⊔-⊓-isLattice : IsLattice _≈₂_ _⊔_ _⊓_) where
     ⟦ y ∧ z ∨ x ⟧                        ≈⟨ ∨-homo (y ∧ z) x ⟩
     ⟦ y ∧ z ⟧ ⊔ ⟦ x ⟧                    ≈⟨ ⊔-congʳ (∧-homo y z) ⟩
     ⟦ y ⟧ ⊓ ⟦ z ⟧ ⊔ ⟦ x ⟧                ≈⟨ distribʳ ⟦ x ⟧ ⟦ y ⟧ ⟦ z ⟧ ⟩
-    (⟦ y ⟧ ⊔ ⟦ x ⟧) ⊓ (⟦ z ⟧ ⊔ ⟦ x ⟧)    ≈˘⟨ ⊓-cong (∨-homo y x) (∨-homo z x) ⟩
-    ⟦ y ∨ x ⟧ ⊓ ⟦ z ∨ x ⟧                ≈˘⟨ ∧-homo (y ∨ x) (z ∨ x) ⟩
+    (⟦ y ⟧ ⊔ ⟦ x ⟧) ⊓ (⟦ z ⟧ ⊔ ⟦ x ⟧)    ≈⟨ ⊓-cong (∨-homo y x) (∨-homo z x) ⟨
+    ⟦ y ∨ x ⟧ ⊓ ⟦ z ∨ x ⟧                ≈⟨ ∧-homo (y ∨ x) (z ∨ x) ⟨
     ⟦ (y ∨ x) ∧ (z ∨ x) ⟧                ∎)
 
 isLattice : IsLattice _≈₂_ _⊔_ _⊓_ → IsLattice _≈₁_ _∨_ _∧_
diff --git a/src/Algebra/Lattice/Properties/BooleanAlgebra.agda b/src/Algebra/Lattice/Properties/BooleanAlgebra.agda
index 85f22c39be..450527ddc0 100644
--- a/src/Algebra/Lattice/Properties/BooleanAlgebra.agda
+++ b/src/Algebra/Lattice/Properties/BooleanAlgebra.agda
@@ -76,8 +76,8 @@ open DistribLatticeProperties distributiveLattice public
 
 ∧-zeroʳ : RightZero ⊥ _∧_
 ∧-zeroʳ x = begin
-  x ∧ ⊥          ≈˘⟨ ∧-congˡ (∧-complementʳ x) ⟩
-  x ∧  x  ∧ ¬ x  ≈˘⟨ ∧-assoc x x (¬ x) ⟩
+  x ∧ ⊥          ≈⟨ ∧-congˡ (∧-complementʳ x) ⟨
+  x ∧  x  ∧ ¬ x  ≈⟨ ∧-assoc x x (¬ x) ⟨
   (x ∧ x) ∧ ¬ x  ≈⟨  ∧-congʳ (∧-idem x) ⟩
   x       ∧ ¬ x  ≈⟨  ∧-complementʳ x ⟩
   ⊥              ∎
@@ -90,8 +90,8 @@ open DistribLatticeProperties distributiveLattice public
 
 ∨-zeroʳ : ∀ x → x ∨ ⊤ ≈ ⊤
 ∨-zeroʳ x = begin
-  x ∨ ⊤          ≈˘⟨ ∨-congˡ (∨-complementʳ x) ⟩
-  x ∨  x  ∨ ¬ x  ≈˘⟨ ∨-assoc x x (¬ x) ⟩
+  x ∨ ⊤          ≈⟨ ∨-congˡ (∨-complementʳ x) ⟨
+  x ∨  x  ∨ ¬ x  ≈⟨ ∨-assoc x x (¬ x) ⟨
   (x ∨ x) ∨ ¬ x  ≈⟨ ∨-congʳ (∨-idem x) ⟩
   x       ∨ ¬ x  ≈⟨ ∨-complementʳ x ⟩
   ⊤              ∎
@@ -182,12 +182,12 @@ open DistribLatticeProperties distributiveLattice public
 private
   lemma : ∀ x y → x ∧ y ≈ ⊥ → x ∨ y ≈ ⊤ → ¬ x ≈ y
   lemma x y x∧y=⊥ x∨y=⊤ = begin
-    ¬ x                ≈˘⟨ ∧-identityʳ _ ⟩
-    ¬ x ∧ ⊤            ≈˘⟨ ∧-congˡ x∨y=⊤ ⟩
+    ¬ x                ≈⟨ ∧-identityʳ _ ⟨
+    ¬ x ∧ ⊤            ≈⟨ ∧-congˡ x∨y=⊤ ⟨
     ¬ x ∧ (x ∨ y)      ≈⟨  ∧-distribˡ-∨ _ _ _ ⟩
     ¬ x ∧ x ∨ ¬ x ∧ y  ≈⟨  ∨-congʳ $ ∧-complementˡ _ ⟩
-    ⊥ ∨ ¬ x ∧ y        ≈˘⟨ ∨-congʳ x∧y=⊥ ⟩
-    x ∧ y ∨ ¬ x ∧ y    ≈˘⟨ ∧-distribʳ-∨ _ _ _ ⟩
+    ⊥ ∨ ¬ x ∧ y        ≈⟨ ∨-congʳ x∧y=⊥ ⟨
+    x ∧ y ∨ ¬ x ∧ y    ≈⟨ ∧-distribʳ-∨ _ _ _ ⟨
     (x ∨ ¬ x) ∧ y      ≈⟨  ∧-congʳ $ ∨-complementʳ _ ⟩
     ⊤ ∧ y              ≈⟨  ∧-identityˡ _ ⟩
     y                  ∎
@@ -222,7 +222,7 @@ deMorgan₁ x y = lemma (x ∧ y) (¬ x ∨ ¬ y) lem₁ lem₂
     ¬ x ∨ y                ∎
 
   lem₂ = begin
-    (x ∧ y) ∨ (¬ x ∨ ¬ y)  ≈˘⟨ ∨-assoc _ _ _ ⟩
+    (x ∧ y) ∨ (¬ x ∨ ¬ y)  ≈⟨ ∨-assoc _ _ _ ⟨
     ((x ∧ y) ∨ ¬ x) ∨ ¬ y  ≈⟨ ∨-congʳ lem₃ ⟩
     (¬ x ∨ y) ∨ ¬ y        ≈⟨ ∨-assoc _ _ _ ⟩
     ¬ x ∨ (y ∨ ¬ y)        ≈⟨ ∨-congˡ $ ∨-complementʳ _ ⟩
@@ -231,8 +231,8 @@ deMorgan₁ x y = lemma (x ∧ y) (¬ x ∨ ¬ y) lem₁ lem₂
 
 deMorgan₂ : ∀ x y → ¬ (x ∨ y) ≈ ¬ x ∧ ¬ y
 deMorgan₂ x y = begin
-  ¬ (x ∨ y)          ≈˘⟨ ¬-cong $ ((¬-involutive _) ⟨ ∨-cong ⟩ (¬-involutive _)) ⟩
-  ¬ (¬ ¬ x ∨ ¬ ¬ y)  ≈˘⟨ ¬-cong $ deMorgan₁ _ _ ⟩
+  ¬ (x ∨ y)          ≈⟨ ¬-cong $ ((¬-involutive _) ⟨ ∨-cong ⟩ (¬-involutive _)) ⟨
+  ¬ (¬ ¬ x ∨ ¬ ¬ y)  ≈⟨ ¬-cong $ deMorgan₁ _ _ ⟨
   ¬ ¬ (¬ x ∧ ¬ y)    ≈⟨ ¬-involutive _ ⟩
   ¬ x ∧ ¬ y          ∎
 
@@ -260,14 +260,14 @@ module XorRing
     x ⊕ u                ≈⟨  ⊕-def _ _ ⟩
     (x ∨ u) ∧ ¬ (x ∧ u)  ≈⟨  helper (x≈y ⟨ ∨-cong ⟩ u≈v)
                                     (x≈y ⟨ ∧-cong ⟩ u≈v) ⟩
-    (y ∨ v) ∧ ¬ (y ∧ v)  ≈˘⟨ ⊕-def _ _ ⟩
+    (y ∨ v) ∧ ¬ (y ∧ v)  ≈⟨ ⊕-def _ _ ⟨
     y ⊕ v                ∎
 
   ⊕-comm : Commutative _⊕_
   ⊕-comm x y = begin
     x ⊕ y                ≈⟨  ⊕-def _ _ ⟩
     (x ∨ y) ∧ ¬ (x ∧ y)  ≈⟨  helper (∨-comm _ _) (∧-comm _ _) ⟩
-    (y ∨ x) ∧ ¬ (y ∧ x)  ≈˘⟨ ⊕-def _ _ ⟩
+    (y ∨ x) ∧ ¬ (y ∧ x)  ≈⟨ ⊕-def _ _ ⟨
     y ⊕ x                ∎
 
   ¬-distribˡ-⊕ : ∀ x y → ¬ (x ⊕ y) ≈ ¬ x ⊕ y
@@ -279,7 +279,7 @@ module XorRing
     ¬ ((x ∧ ¬ y) ∨ (y ∧ ¬ x))              ≈⟨ deMorgan₂ _ _ ⟩
     ¬ (x ∧ ¬ y) ∧ ¬ (y ∧ ¬ x)              ≈⟨ ∧-congʳ $ deMorgan₁ _ _ ⟩
     (¬ x ∨ (¬ ¬ y)) ∧ ¬ (y ∧ ¬ x)          ≈⟨ helper (∨-congˡ $ ¬-involutive _) (∧-comm _ _) ⟩
-    (¬ x ∨ y) ∧ ¬ (¬ x ∧ y)                ≈˘⟨ ⊕-def _ _ ⟩
+    (¬ x ∨ y) ∧ ¬ (¬ x ∧ y)                ≈⟨ ⊕-def _ _ ⟨
     ¬ x ⊕ y                                ∎
     where
     lem : ∀ x y → x ∧ ¬ (x ∧ y) ≈ x ∧ ¬ y
@@ -299,7 +299,7 @@ module XorRing
 
   ⊕-annihilates-¬ : ∀ x y → x ⊕ y ≈ ¬ x ⊕ ¬ y
   ⊕-annihilates-¬ x y = begin
-    x ⊕ y        ≈˘⟨ ¬-involutive _ ⟩
+    x ⊕ y        ≈⟨ ¬-involutive _ ⟨
     ¬ ¬ (x ⊕ y)  ≈⟨  ¬-cong $ ¬-distribˡ-⊕ _ _ ⟩
     ¬ (¬ x ⊕ y)  ≈⟨  ¬-distribʳ-⊕ _ _ ⟩
     ¬ x ⊕ ¬ y    ∎
@@ -334,46 +334,46 @@ module XorRing
   ∧-distribˡ-⊕ : _∧_ DistributesOverˡ _⊕_
   ∧-distribˡ-⊕ x y z = begin
     x ∧ (y ⊕ z)                ≈⟨ ∧-congˡ $ ⊕-def _ _ ⟩
-    x ∧ ((y ∨ z) ∧ ¬ (y ∧ z))  ≈˘⟨ ∧-assoc _ _ _ ⟩
+    x ∧ ((y ∨ z) ∧ ¬ (y ∧ z))  ≈⟨ ∧-assoc _ _ _ ⟨
     (x ∧ (y ∨ z)) ∧ ¬ (y ∧ z)  ≈⟨ ∧-congˡ $ deMorgan₁ _ _ ⟩
     (x ∧ (y ∨ z)) ∧
-    (¬ y ∨ ¬ z)                ≈˘⟨ ∨-identityˡ _ ⟩
+    (¬ y ∨ ¬ z)                ≈⟨ ∨-identityˡ _ ⟨
     ⊥ ∨
     ((x ∧ (y ∨ z)) ∧
     (¬ y ∨ ¬ z))               ≈⟨ ∨-congʳ lem₃ ⟩
     ((x ∧ (y ∨ z)) ∧ ¬ x) ∨
     ((x ∧ (y ∨ z)) ∧
-    (¬ y ∨ ¬ z))               ≈˘⟨ ∧-distribˡ-∨ _ _ _ ⟩
+    (¬ y ∨ ¬ z))               ≈⟨ ∧-distribˡ-∨ _ _ _ ⟨
     (x ∧ (y ∨ z)) ∧
-    (¬ x ∨ (¬ y ∨ ¬ z))        ≈˘⟨ ∧-congˡ $ ∨-congˡ (deMorgan₁ _ _) ⟩
+    (¬ x ∨ (¬ y ∨ ¬ z))        ≈⟨ ∧-congˡ $ ∨-congˡ (deMorgan₁ _ _) ⟨
     (x ∧ (y ∨ z)) ∧
-    (¬ x ∨ ¬ (y ∧ z))          ≈˘⟨ ∧-congˡ (deMorgan₁ _ _) ⟩
+    (¬ x ∨ ¬ (y ∧ z))          ≈⟨ ∧-congˡ (deMorgan₁ _ _) ⟨
     (x ∧ (y ∨ z)) ∧
     ¬ (x ∧ (y ∧ z))            ≈⟨ helper refl lem₁ ⟩
     (x ∧ (y ∨ z)) ∧
     ¬ ((x ∧ y) ∧ (x ∧ z))      ≈⟨ ∧-congʳ $ ∧-distribˡ-∨ _ _ _ ⟩
     ((x ∧ y) ∨ (x ∧ z)) ∧
-    ¬ ((x ∧ y) ∧ (x ∧ z))      ≈˘⟨ ⊕-def _ _ ⟩
+    ¬ ((x ∧ y) ∧ (x ∧ z))      ≈⟨ ⊕-def _ _ ⟨
     (x ∧ y) ⊕ (x ∧ z)          ∎
       where
       lem₂ = begin
-        x ∧ (y ∧ z)  ≈˘⟨ ∧-assoc _ _ _ ⟩
+        x ∧ (y ∧ z)  ≈⟨ ∧-assoc _ _ _ ⟨
         (x ∧ y) ∧ z  ≈⟨ ∧-congʳ $ ∧-comm _ _ ⟩
         (y ∧ x) ∧ z  ≈⟨ ∧-assoc _ _ _ ⟩
         y ∧ (x ∧ z)  ∎
 
       lem₁ = begin
-        x ∧ (y ∧ z)        ≈˘⟨ ∧-congʳ (∧-idem _) ⟩
+        x ∧ (y ∧ z)        ≈⟨ ∧-congʳ (∧-idem _) ⟨
         (x ∧ x) ∧ (y ∧ z)  ≈⟨ ∧-assoc _ _ _ ⟩
         x ∧ (x ∧ (y ∧ z))  ≈⟨ ∧-congˡ lem₂ ⟩
-        x ∧ (y ∧ (x ∧ z))  ≈˘⟨ ∧-assoc _ _ _ ⟩
+        x ∧ (y ∧ (x ∧ z))  ≈⟨ ∧-assoc _ _ _ ⟨
         (x ∧ y) ∧ (x ∧ z)  ∎
 
       lem₃ = begin
-        ⊥                      ≈˘⟨ ∧-zeroʳ _ ⟩
-        (y ∨ z) ∧ ⊥            ≈˘⟨ ∧-congˡ (∧-complementʳ _) ⟩
-        (y ∨ z) ∧ (x ∧ ¬ x)    ≈˘⟨ ∧-assoc _ _ _ ⟩
-        ((y ∨ z) ∧ x) ∧ ¬ x    ≈⟨ ∧-comm _ _ ⟨ ∧-cong ⟩ refl  ⟩
+        ⊥                      ≈⟨ ∧-zeroʳ _ ⟨
+        (y ∨ z) ∧ ⊥            ≈⟨ ∧-congˡ (∧-complementʳ _) ⟨
+        (y ∨ z) ∧ (x ∧ ¬ x)    ≈⟨ ∧-assoc _ _ _ ⟨
+        ((y ∨ z) ∧ x) ∧ ¬ x    ≈⟨ ∧-congʳ (∧-comm _ _) ⟩
         (x ∧ (y ∨ z)) ∧ ¬ x    ∎
 
   ∧-distribʳ-⊕ : _∧_ DistributesOverʳ _⊕_
@@ -398,10 +398,10 @@ module XorRing
 
   ⊕-assoc : Associative _⊕_
   ⊕-assoc x y z = sym $ begin
-    x ⊕ (y ⊕ z)                                ≈⟨ refl ⟨ ⊕-cong ⟩ ⊕-def _ _ ⟩
+    x ⊕ (y ⊕ z)                                ≈⟨ ⊕-cong refl (⊕-def _ _) ⟩
     x ⊕ ((y ∨ z) ∧ ¬ (y ∧ z))                  ≈⟨ ⊕-def _ _ ⟩
       (x ∨ ((y ∨ z) ∧ ¬ (y ∧ z))) ∧
-    ¬ (x ∧ ((y ∨ z) ∧ ¬ (y ∧ z)))              ≈⟨ lem₃ ⟨ ∧-cong ⟩ lem₄ ⟩
+    ¬ (x ∧ ((y ∨ z) ∧ ¬ (y ∧ z)))              ≈⟨ ∧-cong lem₃ lem₄ ⟩
     (((x ∨ y) ∨ z) ∧ ((x ∨ ¬ y) ∨ ¬ z)) ∧
     (((¬ x ∨ ¬ y) ∨ z) ∧ ((¬ x ∨ y) ∨ ¬ z))    ≈⟨ ∧-assoc _ _ _ ⟩
     ((x ∨ y) ∨ z) ∧
@@ -409,40 +409,40 @@ module XorRing
      (((¬ x ∨ ¬ y) ∨ z) ∧ ((¬ x ∨ y) ∨ ¬ z)))  ≈⟨ ∧-congˡ lem₅ ⟩
     ((x ∨ y) ∨ z) ∧
     (((¬ x ∨ ¬ y) ∨ z) ∧
-     (((x ∨ ¬ y) ∨ ¬ z) ∧ ((¬ x ∨ y) ∨ ¬ z)))  ≈˘⟨ ∧-assoc _ _ _ ⟩
+     (((x ∨ ¬ y) ∨ ¬ z) ∧ ((¬ x ∨ y) ∨ ¬ z)))  ≈⟨ ∧-assoc _ _ _ ⟨
     (((x ∨ y) ∨ z) ∧ ((¬ x ∨ ¬ y) ∨ z)) ∧
-    (((x ∨ ¬ y) ∨ ¬ z) ∧ ((¬ x ∨ y) ∨ ¬ z))    ≈⟨ lem₁ ⟨ ∧-cong ⟩ lem₂ ⟩
+    (((x ∨ ¬ y) ∨ ¬ z) ∧ ((¬ x ∨ y) ∨ ¬ z))    ≈⟨ ∧-cong lem₁ lem₂ ⟩
       (((x ∨ y) ∧ ¬ (x ∧ y)) ∨ z) ∧
-    ¬ (((x ∨ y) ∧ ¬ (x ∧ y)) ∧ z)              ≈˘⟨ ⊕-def _ _ ⟩
-    ((x ∨ y) ∧ ¬ (x ∧ y)) ⊕ z                  ≈˘⟨ ⊕-def _ _ ⟨ ⊕-cong ⟩ refl ⟩
+    ¬ (((x ∨ y) ∧ ¬ (x ∧ y)) ∧ z)              ≈⟨ ⊕-def _ _ ⟨
+    ((x ∨ y) ∧ ¬ (x ∧ y)) ⊕ z                  ≈⟨ ⊕-cong (⊕-def _ _) refl ⟨
     (x ⊕ y) ⊕ z                                ∎
     where
     lem₁ = begin
-      ((x ∨ y) ∨ z) ∧ ((¬ x ∨ ¬ y) ∨ z)  ≈˘⟨ ∨-distribʳ-∧ _ _ _ ⟩
-      ((x ∨ y) ∧ (¬ x ∨ ¬ y)) ∨ z        ≈˘⟨ ∨-congʳ $ ∧-congˡ (deMorgan₁ _ _) ⟩
+      ((x ∨ y) ∨ z) ∧ ((¬ x ∨ ¬ y) ∨ z)  ≈⟨ ∨-distribʳ-∧ _ _ _ ⟨
+      ((x ∨ y) ∧ (¬ x ∨ ¬ y)) ∨ z        ≈⟨ ∨-congʳ $ ∧-congˡ (deMorgan₁ _ _) ⟨
       ((x ∨ y) ∧ ¬ (x ∧ y)) ∨ z          ∎
 
     lem₂′ = begin
-      (x ∨ ¬ y) ∧ (¬ x ∨ y)              ≈˘⟨ ∧-identityˡ _ ⟨ ∧-cong ⟩ ∧-identityʳ _ ⟩
-      (⊤ ∧ (x ∨ ¬ y)) ∧ ((¬ x ∨ y) ∧ ⊤)  ≈˘⟨  (∨-complementˡ _ ⟨ ∧-cong ⟩ ∨-comm _ _)
-                                                ⟨ ∧-cong ⟩
-                                              (∧-congˡ $ ∨-complementˡ _) ⟩
+      (x ∨ ¬ y) ∧ (¬ x ∨ y)              ≈⟨ ∧-cong (∧-identityˡ _) (∧-identityʳ _) ⟨
+      (⊤ ∧ (x ∨ ¬ y)) ∧ ((¬ x ∨ y) ∧ ⊤)  ≈⟨ ∧-cong
+                                              (∧-cong (∨-complementˡ _) (∨-comm _ _))
+                                              (∧-congˡ $ ∨-complementˡ _) ⟨
       ((¬ x ∨ x) ∧ (¬ y ∨ x)) ∧
-      ((¬ x ∨ y) ∧ (¬ y ∨ y))            ≈˘⟨ lemma₂ _ _ _ _ ⟩
-      (¬ x ∧ ¬ y) ∨ (x ∧ y)              ≈˘⟨ deMorgan₂ _ _ ⟨ ∨-cong ⟩ ¬-involutive _ ⟩
-      ¬ (x ∨ y) ∨ ¬ ¬ (x ∧ y)            ≈˘⟨ deMorgan₁ _ _ ⟩
+      ((¬ x ∨ y) ∧ (¬ y ∨ y))            ≈⟨ lemma₂ _ _ _ _ ⟨
+      (¬ x ∧ ¬ y) ∨ (x ∧ y)              ≈⟨ ∨-cong (deMorgan₂ _ _) (¬-involutive _) ⟨
+      ¬ (x ∨ y) ∨ ¬ ¬ (x ∧ y)            ≈⟨ deMorgan₁ _ _ ⟨
       ¬ ((x ∨ y) ∧ ¬ (x ∧ y))            ∎
 
     lem₂ = begin
-      ((x ∨ ¬ y) ∨ ¬ z) ∧ ((¬ x ∨ y) ∨ ¬ z)  ≈˘⟨ ∨-distribʳ-∧ _ _ _ ⟩
+      ((x ∨ ¬ y) ∨ ¬ z) ∧ ((¬ x ∨ y) ∨ ¬ z)  ≈⟨ ∨-distribʳ-∧ _ _ _ ⟨
       ((x ∨ ¬ y) ∧ (¬ x ∨ y)) ∨ ¬ z          ≈⟨ ∨-congʳ lem₂′ ⟩
-      ¬ ((x ∨ y) ∧ ¬ (x ∧ y)) ∨ ¬ z          ≈˘⟨ deMorgan₁ _ _ ⟩
+      ¬ ((x ∨ y) ∧ ¬ (x ∧ y)) ∨ ¬ z          ≈⟨ deMorgan₁ _ _ ⟨
       ¬ (((x ∨ y) ∧ ¬ (x ∧ y)) ∧ z)          ∎
 
     lem₃ = begin
       x ∨ ((y ∨ z) ∧ ¬ (y ∧ z))          ≈⟨ ∨-congˡ $ ∧-congˡ $ deMorgan₁ _ _ ⟩
       x ∨ ((y ∨ z) ∧ (¬ y ∨ ¬ z))        ≈⟨ ∨-distribˡ-∧ _ _ _ ⟩
-      (x ∨ (y ∨ z)) ∧ (x ∨ (¬ y ∨ ¬ z))  ≈˘⟨ ∨-assoc _ _ _ ⟨ ∧-cong ⟩ ∨-assoc _ _ _ ⟩
+      (x ∨ (y ∨ z)) ∧ (x ∨ (¬ y ∨ ¬ z))  ≈⟨ ∨-assoc _ _ _ ⟨ ∧-cong ⟩ ∨-assoc _ _ _ ⟨
       ((x ∨ y) ∨ z) ∧ ((x ∨ ¬ y) ∨ ¬ z)  ∎
 
     lem₄′ = begin
@@ -462,7 +462,7 @@ module XorRing
       ¬ x ∨ ¬ ((y ∨ z) ∧ ¬ (y ∧ z))  ≈⟨ ∨-congˡ lem₄′ ⟩
       ¬ x ∨ ((y ∨ ¬ z) ∧ (¬ y ∨ z))  ≈⟨ ∨-distribˡ-∧ _ _ _ ⟩
       (¬ x ∨ (y     ∨ ¬ z)) ∧
-      (¬ x ∨ (¬ y ∨ z))              ≈˘⟨ ∨-assoc _ _ _ ⟨ ∧-cong ⟩ ∨-assoc _ _ _ ⟩
+      (¬ x ∨ (¬ y ∨ z))              ≈⟨ ∨-assoc _ _ _ ⟨ ∧-cong ⟩ ∨-assoc _ _ _ ⟨
       ((¬ x ∨ y)     ∨ ¬ z) ∧
       ((¬ x ∨ ¬ y) ∨ z)              ≈⟨ ∧-comm _ _ ⟩
       ((¬ x ∨ ¬ y) ∨ z) ∧
@@ -470,7 +470,7 @@ module XorRing
 
     lem₅ = begin
       ((x ∨ ¬ y) ∨ ¬ z) ∧
-      (((¬ x ∨ ¬ y) ∨ z) ∧ ((¬ x ∨ y) ∨ ¬ z))    ≈˘⟨ ∧-assoc _ _ _ ⟩
+      (((¬ x ∨ ¬ y) ∨ z) ∧ ((¬ x ∨ y) ∨ ¬ z))    ≈⟨ ∧-assoc _ _ _ ⟨
       (((x ∨ ¬ y) ∨ ¬ z) ∧ ((¬ x ∨ ¬ y) ∨ z)) ∧
       ((¬ x ∨ y) ∨ ¬ z)                          ≈⟨ ∧-congʳ $ ∧-comm _ _ ⟩
       (((¬ x ∨ ¬ y) ∨ z) ∧ ((x ∨ ¬ y) ∨ ¬ z)) ∧
diff --git a/src/Algebra/Lattice/Properties/Lattice.agda b/src/Algebra/Lattice/Properties/Lattice.agda
index b83dcdea10..281330ef15 100644
--- a/src/Algebra/Lattice/Properties/Lattice.agda
+++ b/src/Algebra/Lattice/Properties/Lattice.agda
@@ -27,7 +27,7 @@ open import Relation.Binary.Reasoning.Setoid setoid
 
 ∧-idem : Idempotent _∧_
 ∧-idem x = begin
-  x ∧ x            ≈˘⟨ ∧-congˡ (∨-absorbs-∧ _ _) ⟩
+  x ∧ x            ≈⟨ ∧-congˡ (∨-absorbs-∧ _ _) ⟨
   x ∧ (x ∨ x ∧ x)  ≈⟨  ∧-absorbs-∨ _ _ ⟩
   x                ∎
 
@@ -73,7 +73,7 @@ open SemilatticeProperties ∧-semilattice public
 
 ∨-idem : Idempotent _∨_
 ∨-idem x = begin
-  x ∨ x      ≈˘⟨ ∨-congˡ (∧-idem _) ⟩
+  x ∨ x      ≈⟨ ∨-congˡ (∧-idem _) ⟨
   x ∨ x ∧ x  ≈⟨  ∨-absorbs-∧ _ _ ⟩
   x          ∎
 
diff --git a/src/Algebra/Module/Consequences.agda b/src/Algebra/Module/Consequences.agda
index 2e53f96d76..9acd6d6413 100644
--- a/src/Algebra/Module/Consequences.agda
+++ b/src/Algebra/Module/Consequences.agda
@@ -45,7 +45,7 @@ module _ (_≈ᴬ_ : Rel {a} A ℓa) (S : Setoid c ℓ) where
       L.Associative _*_ _*ₗ_ → Commutative _*_ → R.Associative _*_ _*ᵣ_
     *ₗ-assoc+comm⇒*ᵣ-assoc *ₗ-congʳ *ₗ-assoc *-comm m x y = begin
       (m *ᵣ x) *ᵣ y  ≈⟨ refl ⟩
-      y *ₗ (x *ₗ m)  ≈˘⟨ *ₗ-assoc _ _ _ ⟩
+      y *ₗ (x *ₗ m)  ≈⟨ *ₗ-assoc _ _ _ ⟨
       (y * x) *ₗ m   ≈⟨ *ₗ-congʳ (*-comm y x) ⟩
       (x * y) *ₗ m   ≈⟨ refl ⟩
       m *ᵣ (x * y)   ∎
@@ -55,7 +55,7 @@ module _ (_≈ᴬ_ : Rel {a} A ℓa) (S : Setoid c ℓ) where
       L.Associative _*_ _*ₗ_ → Commutative _*_ → B.Associative _*ₗ_ _*ᵣ_
     *ₗ-assoc+comm⇒*ₗ-*ᵣ-assoc *ₗ-congʳ *ₗ-assoc *-comm x m y = begin
       ((x *ₗ m) *ᵣ y)  ≈⟨ refl ⟩
-      (y *ₗ (x *ₗ m))  ≈˘⟨ *ₗ-assoc _ _ _ ⟩
+      (y *ₗ (x *ₗ m))  ≈⟨ *ₗ-assoc _ _ _ ⟨
       ((y * x) *ₗ m)   ≈⟨ *ₗ-congʳ (*-comm y x) ⟩
       ((x * y) *ₗ m)   ≈⟨ *ₗ-assoc _ _ _ ⟩
       (x *ₗ (y *ₗ m))  ≈⟨ refl ⟩
@@ -72,7 +72,7 @@ module _ (_≈ᴬ_ : Rel {a} A ℓa) (S : Setoid c ℓ) where
     *ᵣ-assoc+comm⇒*ₗ-assoc *ᵣ-congˡ *ᵣ-assoc *-comm x y m = begin
       ((x * y) *ₗ m)   ≈⟨ refl ⟩
       (m *ᵣ (x * y))   ≈⟨ *ᵣ-congˡ (*-comm x y) ⟩
-      (m *ᵣ (y * x))   ≈˘⟨ *ᵣ-assoc _ _ _ ⟩
+      (m *ᵣ (y * x))   ≈⟨ *ᵣ-assoc _ _ _ ⟨
       ((m *ᵣ y) *ᵣ x)  ≈⟨ refl ⟩
       (x *ₗ (y *ₗ m))  ∎
 
@@ -83,6 +83,6 @@ module _ (_≈ᴬ_ : Rel {a} A ℓa) (S : Setoid c ℓ) where
       ((x *ₗ m) *ᵣ y)  ≈⟨ refl ⟩
       ((m *ᵣ x) *ᵣ y)  ≈⟨ *ᵣ-assoc _ _ _ ⟩
       (m *ᵣ (x * y))   ≈⟨ *ᵣ-congˡ (*-comm x y) ⟩
-      (m *ᵣ (y * x))   ≈˘⟨ *ᵣ-assoc _ _ _ ⟩
+      (m *ᵣ (y * x))   ≈⟨ *ᵣ-assoc _ _ _ ⟨
       ((m *ᵣ y) *ᵣ x)  ≈⟨ refl ⟩
       (x *ₗ (m *ᵣ y))  ∎
diff --git a/src/Algebra/Morphism/Consequences.agda b/src/Algebra/Morphism/Consequences.agda
index 96175740e6..e297a8dbc9 100644
--- a/src/Algebra/Morphism/Consequences.agda
+++ b/src/Algebra/Morphism/Consequences.agda
@@ -30,8 +30,8 @@ module _ {α α= β β=} (M₁ : Magma α α=) (M₂ : Magma β β=) where
                       Homomorphic₂ _ _ _≈₂_ f _∙₁_ _∙₂_  →
                       Homomorphic₂ _ _ _≈₁_ g _∙₂_ _∙₁_
   homomorphic₂-inv {f} {g} g-cong (invˡ , invʳ) homo x y = begin
-    g (x ∙₂ y)             ≈˘⟨ g-cong (M₂.∙-cong (invˡ M₁.refl) (invˡ M₁.refl)) ⟩
-    g (f (g x) ∙₂ f (g y)) ≈˘⟨ g-cong (homo (g x) (g y)) ⟩
+    g (x ∙₂ y)             ≈⟨ g-cong (M₂.∙-cong (invˡ M₁.refl) (invˡ M₁.refl)) ⟨
+    g (f (g x) ∙₂ f (g y)) ≈⟨ g-cong (homo (g x) (g y)) ⟨
     g (f (g x ∙₁ g y))     ≈⟨ invʳ M₂.refl ⟩
     g x ∙₁ g y             ∎
     where open EqR M₁.setoid
@@ -42,7 +42,7 @@ module _ {α α= β β=} (M₁ : Magma α α=) (M₂ : Magma β β=) where
                       Homomorphic₂ _ _ _≈₁_ g _∙₂_ _∙₁_
   homomorphic₂-inj {f} {g} inj invˡ homo x y = inj (begin
     f (g (x ∙₂ y))      ≈⟨ invˡ M₁.refl ⟩
-    x ∙₂ y              ≈˘⟨ M₂.∙-cong (invˡ M₁.refl) (invˡ M₁.refl) ⟩
-    f (g x) ∙₂ f (g y)  ≈˘⟨ homo (g x) (g y) ⟩
+    x ∙₂ y              ≈⟨ M₂.∙-cong (invˡ M₁.refl) (invˡ M₁.refl) ⟨
+    f (g x) ∙₂ f (g y)  ≈⟨ homo (g x) (g y) ⟨
     f (g x ∙₁ g y)      ∎)
     where open EqR M₂.setoid
diff --git a/src/Algebra/Morphism/GroupMonomorphism.agda b/src/Algebra/Morphism/GroupMonomorphism.agda
index b862559938..51cdcbafe7 100644
--- a/src/Algebra/Morphism/GroupMonomorphism.agda
+++ b/src/Algebra/Morphism/GroupMonomorphism.agda
@@ -48,7 +48,7 @@ module _ (◦-isMagma : IsMagma _≈₂_ _◦_) where
     ⟦ x ⁻¹₁ ∙ x ⟧     ≈⟨ ∙-homo (x ⁻¹₁ ) x ⟩
     ⟦ x ⁻¹₁ ⟧ ◦ ⟦ x ⟧ ≈⟨ ◦-cong (⁻¹-homo x) refl ⟩
     ⟦ x ⟧ ⁻¹₂ ◦ ⟦ x ⟧ ≈⟨ invˡ ⟦ x ⟧ ⟩
-    ε₂                ≈˘⟨ ε-homo ⟩
+    ε₂                ≈⟨ ε-homo ⟨
     ⟦ ε₁ ⟧ ∎)
 
   inverseʳ : RightInverse _≈₂_ ε₂ _⁻¹₂ _◦_ → RightInverse _≈₁_ ε₁ _⁻¹₁ _∙_
@@ -56,7 +56,7 @@ module _ (◦-isMagma : IsMagma _≈₂_ _◦_) where
     ⟦ x ∙ x ⁻¹₁ ⟧     ≈⟨ ∙-homo x (x ⁻¹₁) ⟩
     ⟦ x ⟧ ◦ ⟦ x ⁻¹₁ ⟧ ≈⟨ ◦-cong refl (⁻¹-homo x) ⟩
     ⟦ x ⟧ ◦ ⟦ x ⟧ ⁻¹₂ ≈⟨ invʳ ⟦ x ⟧ ⟩
-    ε₂                ≈˘⟨ ε-homo ⟩
+    ε₂                ≈⟨ ε-homo ⟨
     ⟦ ε₁ ⟧ ∎)
 
   inverse : Inverse _≈₂_ ε₂ _⁻¹₂ _◦_ → Inverse _≈₁_ ε₁ _⁻¹₁ _∙_
@@ -66,7 +66,7 @@ module _ (◦-isMagma : IsMagma _≈₂_ _◦_) where
   ⁻¹-cong ⁻¹-cong {x} {y} x≈y = injective (begin
     ⟦ x ⁻¹₁ ⟧ ≈⟨ ⁻¹-homo x ⟩
     ⟦ x ⟧ ⁻¹₂ ≈⟨ ⁻¹-cong (⟦⟧-cong x≈y) ⟩
-    ⟦ y ⟧ ⁻¹₂ ≈˘⟨ ⁻¹-homo y ⟩
+    ⟦ y ⟧ ⁻¹₂ ≈⟨ ⁻¹-homo y ⟨
     ⟦ y ⁻¹₁ ⟧ ∎)
 
 module _ (◦-isAbelianGroup : IsAbelianGroup _≈₂_ _◦_ ε₂ _⁻¹₂) where
diff --git a/src/Algebra/Morphism/MagmaMonomorphism.agda b/src/Algebra/Morphism/MagmaMonomorphism.agda
index 30f19edb02..87027ba5e1 100644
--- a/src/Algebra/Morphism/MagmaMonomorphism.agda
+++ b/src/Algebra/Morphism/MagmaMonomorphism.agda
@@ -42,7 +42,7 @@ module _ (◦-isMagma : IsMagma _≈₂_ _◦_) where
   cong {x} {y} {u} {v} x≈y u≈v = injective (begin
     ⟦ x ∙ u ⟧      ≈⟨  homo x u ⟩
     ⟦ x ⟧ ◦ ⟦ u ⟧  ≈⟨  ◦-cong (⟦⟧-cong x≈y) (⟦⟧-cong u≈v) ⟩
-    ⟦ y ⟧ ◦ ⟦ v ⟧  ≈˘⟨ homo y v ⟩
+    ⟦ y ⟧ ◦ ⟦ v ⟧  ≈⟨ homo y v ⟨
     ⟦ y ∙ v ⟧      ∎)
 
   assoc : Associative _≈₂_ _◦_ → Associative _≈₁_ _∙_
@@ -50,15 +50,15 @@ module _ (◦-isMagma : IsMagma _≈₂_ _◦_) where
     ⟦ (x ∙ y) ∙ z ⟧          ≈⟨  homo (x ∙ y) z ⟩
     ⟦ x ∙ y ⟧ ◦ ⟦ z ⟧        ≈⟨  ◦-cong (homo x y) refl ⟩
     (⟦ x ⟧ ◦ ⟦ y ⟧) ◦ ⟦ z ⟧  ≈⟨  assoc ⟦ x ⟧ ⟦ y ⟧ ⟦ z ⟧ ⟩
-    ⟦ x ⟧ ◦ (⟦ y ⟧ ◦ ⟦ z ⟧)  ≈˘⟨ ◦-cong refl (homo y z) ⟩
-    ⟦ x ⟧ ◦ ⟦ y ∙ z ⟧        ≈˘⟨ homo x (y ∙ z) ⟩
+    ⟦ x ⟧ ◦ (⟦ y ⟧ ◦ ⟦ z ⟧)  ≈⟨ ◦-cong refl (homo y z) ⟨
+    ⟦ x ⟧ ◦ ⟦ y ∙ z ⟧        ≈⟨ homo x (y ∙ z) ⟨
     ⟦ x ∙ (y ∙ z) ⟧          ∎)
 
   comm : Commutative _≈₂_ _◦_ → Commutative _≈₁_ _∙_
   comm comm x y = injective (begin
     ⟦ x ∙ y ⟧      ≈⟨  homo x y ⟩
     ⟦ x ⟧ ◦ ⟦ y ⟧  ≈⟨  comm ⟦ x ⟧ ⟦ y ⟧ ⟩
-    ⟦ y ⟧ ◦ ⟦ x ⟧  ≈˘⟨ homo y x ⟩
+    ⟦ y ⟧ ◦ ⟦ x ⟧  ≈⟨ homo y x ⟨
     ⟦ y ∙ x ⟧      ∎)
 
   idem : Idempotent _≈₂_ _◦_ → Idempotent _≈₁_ _∙_
@@ -80,14 +80,14 @@ module _ (◦-isMagma : IsMagma _≈₂_ _◦_) where
 
   cancelˡ : LeftCancellative _≈₂_ _◦_ → LeftCancellative _≈₁_ _∙_
   cancelˡ cancelˡ x y z x∙y≈x∙z = injective (cancelˡ ⟦ x ⟧ ⟦ y ⟧ ⟦ z ⟧ (begin
-    ⟦ x ⟧ ◦ ⟦ y ⟧  ≈˘⟨ homo x y ⟩
+    ⟦ x ⟧ ◦ ⟦ y ⟧  ≈⟨ homo x y ⟨
     ⟦ x ∙ y ⟧      ≈⟨  ⟦⟧-cong x∙y≈x∙z ⟩
     ⟦ x ∙ z ⟧      ≈⟨  homo x z ⟩
     ⟦ x ⟧ ◦ ⟦ z ⟧  ∎))
 
   cancelʳ : RightCancellative _≈₂_ _◦_ → RightCancellative _≈₁_ _∙_
   cancelʳ cancelʳ x y z y∙x≈z∙x = injective (cancelʳ ⟦ x ⟧ ⟦ y ⟧ ⟦ z ⟧ (begin
-    ⟦ y ⟧ ◦ ⟦ x ⟧  ≈˘⟨ homo y x ⟩
+    ⟦ y ⟧ ◦ ⟦ x ⟧  ≈⟨ homo y x ⟨
     ⟦ y ∙ x ⟧      ≈⟨  ⟦⟧-cong y∙x≈z∙x ⟩
     ⟦ z ∙ x ⟧      ≈⟨  homo z x ⟩
     ⟦ z ⟧ ◦ ⟦ x ⟧  ∎))
diff --git a/src/Algebra/Morphism/MonoidMonomorphism.agda b/src/Algebra/Morphism/MonoidMonomorphism.agda
index 4a512b2687..bfb412302e 100644
--- a/src/Algebra/Morphism/MonoidMonomorphism.agda
+++ b/src/Algebra/Morphism/MonoidMonomorphism.agda
@@ -63,7 +63,7 @@ module _ (◦-isMagma : IsMagma _≈₂_ _◦_) where
     ⟦ ε₁ ∙ x ⟧     ≈⟨  homo ε₁ x ⟩
     ⟦ ε₁ ⟧ ◦ ⟦ x ⟧ ≈⟨  ◦-cong ε-homo refl ⟩
     ε₂   ◦ ⟦ x ⟧   ≈⟨  zeˡ ⟦ x ⟧ ⟩
-    ε₂             ≈˘⟨ ε-homo ⟩
+    ε₂             ≈⟨ ε-homo ⟨
     ⟦ ε₁ ⟧         ∎)
 
   zeroʳ : RightZero _≈₂_ ε₂ _◦_ → RightZero _≈₁_ ε₁ _∙_
@@ -71,7 +71,7 @@ module _ (◦-isMagma : IsMagma _≈₂_ _◦_) where
     ⟦ x ∙ ε₁ ⟧     ≈⟨  homo x ε₁ ⟩
     ⟦ x ⟧ ◦ ⟦ ε₁ ⟧ ≈⟨  ◦-cong refl ε-homo ⟩
     ⟦ x ⟧ ◦ ε₂     ≈⟨  zeʳ ⟦ x ⟧ ⟩
-    ε₂             ≈˘⟨ ε-homo ⟩
+    ε₂             ≈⟨ ε-homo ⟨
     ⟦ ε₁ ⟧         ∎)
 
   zero : Zero _≈₂_ ε₂ _◦_ → Zero _≈₁_ ε₁ _∙_
diff --git a/src/Algebra/Morphism/RingMonomorphism.agda b/src/Algebra/Morphism/RingMonomorphism.agda
index 4b2c900946..9230c802a9 100644
--- a/src/Algebra/Morphism/RingMonomorphism.agda
+++ b/src/Algebra/Morphism/RingMonomorphism.agda
@@ -90,8 +90,8 @@ module _ (+-isGroup : IsGroup _≈₂_ _⊕_ 0#₂ ⊝_)
     ⟦ x * (y + z) ⟧               ≈⟨ *-homo x (y + z) ⟩
     ⟦ x ⟧ ⊛ ⟦ y + z ⟧             ≈⟨ ◦-cong refl (+-homo y z) ⟩
     ⟦ x ⟧ ⊛ (⟦ y ⟧ ⊕ ⟦ z ⟧)       ≈⟨ distribˡ ⟦ x ⟧ ⟦ y ⟧ ⟦ z ⟧ ⟩
-    ⟦ x ⟧ ⊛ ⟦ y ⟧ ⊕ ⟦ x ⟧ ⊛ ⟦ z ⟧ ≈˘⟨ ∙-cong (*-homo x y) (*-homo x z) ⟩
-    ⟦ x * y ⟧ ⊕ ⟦ x * z ⟧         ≈˘⟨ +-homo (x * y) (x * z) ⟩
+    ⟦ x ⟧ ⊛ ⟦ y ⟧ ⊕ ⟦ x ⟧ ⊛ ⟦ z ⟧ ≈⟨ ∙-cong (*-homo x y) (*-homo x z) ⟨
+    ⟦ x * y ⟧ ⊕ ⟦ x * z ⟧         ≈⟨ +-homo (x * y) (x * z) ⟨
     ⟦ x * y + x * z ⟧ ∎)
 
   distribʳ : _DistributesOverʳ_ _≈₂_ _⊛_ _⊕_ → _DistributesOverʳ_ _≈₁_ _*_ _+_
@@ -99,8 +99,8 @@ module _ (+-isGroup : IsGroup _≈₂_ _⊕_ 0#₂ ⊝_)
     ⟦ (y + z) * x ⟧               ≈⟨ *-homo (y + z) x ⟩
     ⟦ y + z ⟧ ⊛ ⟦ x ⟧             ≈⟨ ◦-cong (+-homo y z) refl ⟩
     (⟦ y ⟧ ⊕ ⟦ z ⟧) ⊛ ⟦ x ⟧       ≈⟨ distribˡ ⟦ x ⟧ ⟦ y ⟧ ⟦ z ⟧ ⟩
-    ⟦ y ⟧ ⊛ ⟦ x ⟧ ⊕ ⟦ z ⟧ ⊛ ⟦ x ⟧ ≈˘⟨ ∙-cong (*-homo y x) (*-homo z x) ⟩
-    ⟦ y * x ⟧ ⊕ ⟦ z * x ⟧         ≈˘⟨ +-homo (y * x) (z * x) ⟩
+    ⟦ y ⟧ ⊛ ⟦ x ⟧ ⊕ ⟦ z ⟧ ⊛ ⟦ x ⟧ ≈⟨ ∙-cong (*-homo y x) (*-homo z x) ⟨
+    ⟦ y * x ⟧ ⊕ ⟦ z * x ⟧         ≈⟨ +-homo (y * x) (z * x) ⟨
     ⟦ y * x + z * x ⟧ ∎)
 
   distrib : _DistributesOver_ _≈₂_ _⊛_ _⊕_ → _DistributesOver_ _≈₁_ _*_ _+_
@@ -111,7 +111,7 @@ module _ (+-isGroup : IsGroup _≈₂_ _⊕_ 0#₂ ⊝_)
     ⟦ 0# * x ⟧     ≈⟨ *-homo 0# x ⟩
     ⟦ 0# ⟧ ⊛ ⟦ x ⟧ ≈⟨ ◦-cong 0#-homo refl ⟩
     0#₂ ⊛ ⟦ x ⟧    ≈⟨ zeroˡ ⟦ x ⟧ ⟩
-    0#₂            ≈˘⟨ 0#-homo ⟩
+    0#₂            ≈⟨ 0#-homo ⟨
     ⟦ 0# ⟧         ∎)
 
   zeroʳ : RightZero _≈₂_ 0#₂ _⊛_ → RightZero _≈₁_ 0# _*_
@@ -119,7 +119,7 @@ module _ (+-isGroup : IsGroup _≈₂_ _⊕_ 0#₂ ⊝_)
     ⟦ x * 0# ⟧     ≈⟨ *-homo x 0# ⟩
     ⟦ x ⟧ ⊛ ⟦ 0# ⟧ ≈⟨ ◦-cong refl 0#-homo ⟩
     ⟦ x ⟧ ⊛ 0#₂    ≈⟨ zeroʳ ⟦ x ⟧ ⟩
-    0#₂            ≈˘⟨ 0#-homo ⟩
+    0#₂            ≈⟨ 0#-homo ⟨
     ⟦ 0# ⟧         ∎)
 
   zero : Zero _≈₂_ 0#₂ _⊛_ → Zero _≈₁_ 0# _*_
diff --git a/src/Algebra/Properties/AbelianGroup.agda b/src/Algebra/Properties/AbelianGroup.agda
index 6846f29d83..87c6b7c6b9 100644
--- a/src/Algebra/Properties/AbelianGroup.agda
+++ b/src/Algebra/Properties/AbelianGroup.agda
@@ -33,6 +33,6 @@ xyx⁻¹≈y x y = begin
 
 ⁻¹-∙-comm : ∀ x y → x ⁻¹ ∙ y ⁻¹ ≈ (x ∙ y) ⁻¹
 ⁻¹-∙-comm x y = begin
-  x ⁻¹ ∙ y ⁻¹ ≈˘⟨ ⁻¹-anti-homo-∙ y x ⟩
+  x ⁻¹ ∙ y ⁻¹ ≈⟨ ⁻¹-anti-homo-∙ y x ⟨
   (y ∙ x) ⁻¹  ≈⟨ ⁻¹-cong $ comm y x ⟩
   (x ∙ y) ⁻¹  ∎
diff --git a/src/Algebra/Properties/CommutativeMonoid/Mult/TCOptimised.agda b/src/Algebra/Properties/CommutativeMonoid/Mult/TCOptimised.agda
index 8985fb21cb..0774e5d7a1 100644
--- a/src/Algebra/Properties/CommutativeMonoid/Mult/TCOptimised.agda
+++ b/src/Algebra/Properties/CommutativeMonoid/Mult/TCOptimised.agda
@@ -40,7 +40,7 @@ open import Algebra.Properties.Monoid.Mult.TCOptimised monoid public
 
 ×-distrib-+ : ∀ x y n → n × (x + y) ≈ n × x + n × y
 ×-distrib-+ x y n = begin
-  n ×  (x + y)    ≈˘⟨ ×ᵤ≈× n (x + y) ⟩
+  n ×  (x + y)    ≈⟨ ×ᵤ≈× n (x + y) ⟨
   n ×ᵤ (x + y)    ≈⟨  U.×-distrib-+ x y n ⟩
   n ×ᵤ x + n ×ᵤ y ≈⟨  +-cong (×ᵤ≈× n x) (×ᵤ≈× n y) ⟩
   n ×  x + n ×  y ∎
diff --git a/src/Algebra/Properties/CommutativeMonoid/Sum.agda b/src/Algebra/Properties/CommutativeMonoid/Sum.agda
index 5873d4eb61..eed54de4ed 100644
--- a/src/Algebra/Properties/CommutativeMonoid/Sum.agda
+++ b/src/Algebra/Properties/CommutativeMonoid/Sum.agda
@@ -90,9 +90,9 @@ sum-permute {zero}  {suc n} f π = contradiction π (Perm.refute λ())
 sum-permute {suc m} {zero}  f π = contradiction π (Perm.refute λ())
 sum-permute {suc m} {suc n} f π = begin
   sum f                                    ≡⟨⟩
-  f 0F  + sum f/0                          ≡˘⟨ P.cong (_+ sum f/0) (P.cong f (Perm.inverseʳ π)) ⟩
+  f 0F  + sum f/0                          ≡⟨ P.cong (_+ sum f/0) (P.cong f (Perm.inverseʳ π)) ⟨
   πf π₀ + sum f/0                          ≈⟨ +-congˡ (sum-permute f/0 (Perm.remove π₀ π)) ⟩
-  πf π₀ + sum (rearrange (π/0 ⟨$⟩ʳ_) f/0)  ≡˘⟨ P.cong (πf π₀ +_) (sum-cong-≗ (P.cong f ∘ Perm.punchIn-permute′ π 0F)) ⟩
+  πf π₀ + sum (rearrange (π/0 ⟨$⟩ʳ_) f/0)  ≡⟨ P.cong (πf π₀ +_) (sum-cong-≗ (P.cong f ∘ Perm.punchIn-permute′ π 0F)) ⟨
   πf π₀ + sum (removeAt πf π₀)             ≈⟨ sym (sum-remove πf) ⟩
   sum πf                                   ∎
   where
diff --git a/src/Algebra/Properties/CommutativeSemigroup.agda b/src/Algebra/Properties/CommutativeSemigroup.agda
index 0c27a5e96b..bcfee1fec2 100644
--- a/src/Algebra/Properties/CommutativeSemigroup.agda
+++ b/src/Algebra/Properties/CommutativeSemigroup.agda
@@ -29,10 +29,10 @@ open import Algebra.Properties.Semigroup semigroup public
 interchange : Interchangable _∙_ _∙_
 interchange a b c d = begin
   (a ∙ b) ∙ (c ∙ d)  ≈⟨  assoc a b (c ∙ d) ⟩
-  a ∙ (b ∙ (c ∙ d))  ≈˘⟨ ∙-congˡ (assoc b c d) ⟩
+  a ∙ (b ∙ (c ∙ d))  ≈⟨ ∙-congˡ (assoc b c d) ⟨
   a ∙ ((b ∙ c) ∙ d)  ≈⟨  ∙-congˡ (∙-congʳ (comm b c)) ⟩
   a ∙ ((c ∙ b) ∙ d)  ≈⟨  ∙-congˡ (assoc c b d) ⟩
-  a ∙ (c ∙ (b ∙ d))  ≈˘⟨ assoc a c (b ∙ d) ⟩
+  a ∙ (c ∙ (b ∙ d))  ≈⟨ assoc a c (b ∙ d) ⟨
   (a ∙ c) ∙ (b ∙ d)  ∎
 
 ------------------------------------------------------------------------
diff --git a/src/Algebra/Properties/Group.agda b/src/Algebra/Properties/Group.agda
index 7cdf88c9fe..31f9aedf39 100644
--- a/src/Algebra/Properties/Group.agda
+++ b/src/Algebra/Properties/Group.agda
@@ -42,14 +42,14 @@ private
 ∙-cancelˡ x y z eq = begin
               y  ≈⟨ right-helper x y ⟩
   x ⁻¹ ∙ (x ∙ y) ≈⟨ ∙-congˡ eq ⟩
-  x ⁻¹ ∙ (x ∙ z) ≈˘⟨ right-helper x z ⟩
+  x ⁻¹ ∙ (x ∙ z) ≈⟨ right-helper x z ⟨
               z  ∎
 
 ∙-cancelʳ : RightCancellative _∙_
 ∙-cancelʳ x y z eq = begin
   y            ≈⟨ left-helper y x ⟩
   y ∙ x ∙ x ⁻¹ ≈⟨ ∙-congʳ eq ⟩
-  z ∙ x ∙ x ⁻¹ ≈˘⟨ left-helper z x ⟩
+  z ∙ x ∙ x ⁻¹ ≈⟨ left-helper z x ⟨
   z            ∎
 
 ∙-cancel : Cancellative _∙_
@@ -57,22 +57,22 @@ private
 
 ⁻¹-involutive : ∀ x → x ⁻¹ ⁻¹ ≈ x
 ⁻¹-involutive x = begin
-  x ⁻¹ ⁻¹              ≈˘⟨ identityʳ _ ⟩
-  x ⁻¹ ⁻¹ ∙ ε          ≈˘⟨ ∙-congˡ $ inverseˡ _ ⟩
-  x ⁻¹ ⁻¹ ∙ (x ⁻¹ ∙ x) ≈˘⟨ right-helper (x ⁻¹) x ⟩
+  x ⁻¹ ⁻¹              ≈⟨ identityʳ _ ⟨
+  x ⁻¹ ⁻¹ ∙ ε          ≈⟨ ∙-congˡ $ inverseˡ _ ⟨
+  x ⁻¹ ⁻¹ ∙ (x ⁻¹ ∙ x) ≈⟨ right-helper (x ⁻¹) x ⟨
   x                    ∎
 
 ⁻¹-injective : ∀ {x y} → x ⁻¹ ≈ y ⁻¹ → x ≈ y
 ⁻¹-injective {x} {y} eq = ∙-cancelʳ _ _ _ ( begin
   x ∙ x ⁻¹ ≈⟨ inverseʳ x ⟩
-  ε        ≈˘⟨ inverseʳ y ⟩
-  y ∙ y ⁻¹ ≈˘⟨ ∙-congˡ eq ⟩
+  ε        ≈⟨ inverseʳ y ⟨
+  y ∙ y ⁻¹ ≈⟨ ∙-congˡ eq ⟨
   y ∙ x ⁻¹ ∎ )
 
 ⁻¹-anti-homo-∙ : ∀ x y → (x ∙ y) ⁻¹ ≈ y ⁻¹ ∙ x ⁻¹
 ⁻¹-anti-homo-∙ x y = ∙-cancelˡ _ _ _ ( begin
   x ∙ y ∙ (x ∙ y) ⁻¹    ≈⟨ inverseʳ _ ⟩
-  ε                     ≈˘⟨ inverseʳ _ ⟩
+  ε                     ≈⟨ inverseʳ _ ⟨
   x ∙ x ⁻¹              ≈⟨ ∙-congʳ (left-helper x y) ⟩
   (x ∙ y) ∙ y ⁻¹ ∙ x ⁻¹ ≈⟨ assoc (x ∙ y) (y ⁻¹) (x ⁻¹) ⟩
   x ∙ y ∙ (y ⁻¹ ∙ x ⁻¹) ∎ )
diff --git a/src/Algebra/Properties/Monoid/Mult.agda b/src/Algebra/Properties/Monoid/Mult.agda
index 7abdb583ca..88c4258fcb 100644
--- a/src/Algebra/Properties/Monoid/Mult.agda
+++ b/src/Algebra/Properties/Monoid/Mult.agda
@@ -70,5 +70,5 @@ open import Algebra.Definitions.RawMonoid rawMonoid public
 ×-assocˡ x zero    n = refl
 ×-assocˡ x (suc m) n = begin
   n × x + m × n × x     ≈⟨ +-congˡ (×-assocˡ x m n) ⟩
-  n × x + (m ℕ.* n) × x ≈˘⟨ ×-homo-+ x n (m ℕ.* n) ⟩
+  n × x + (m ℕ.* n) × x ≈⟨ ×-homo-+ x n (m ℕ.* n) ⟨
   (suc m ℕ.* n) × x     ∎
diff --git a/src/Algebra/Properties/Monoid/Mult/TCOptimised.agda b/src/Algebra/Properties/Monoid/Mult/TCOptimised.agda
index ded5f1339e..c862c5e3f2 100644
--- a/src/Algebra/Properties/Monoid/Mult/TCOptimised.agda
+++ b/src/Algebra/Properties/Monoid/Mult/TCOptimised.agda
@@ -55,14 +55,14 @@ open import Algebra.Definitions.RawMonoid rawMonoid public
 ×ᵤ≈× 0       x = refl
 ×ᵤ≈× (suc n) x = begin
   x + n ×ᵤ x  ≈⟨ +-congˡ (×ᵤ≈× n x) ⟩
-  x + n ×  x  ≈˘⟨ 1+× n x ⟩
+  x + n ×  x  ≈⟨ 1+× n x ⟨
   suc n ×  x  ∎
 
 -- _×_ is homomorphic with respect to _ℕ.+_/_+_.
 
 ×-homo-+ : ∀ c m n → (m ℕ.+ n) × c ≈ m × c + n × c
 ×-homo-+ c m n = begin
-  (m ℕ.+ n) ×  c   ≈˘⟨ ×ᵤ≈× (m ℕ.+ n) c ⟩
+  (m ℕ.+ n) ×  c   ≈⟨ ×ᵤ≈× (m ℕ.+ n) c ⟨
   (m ℕ.+ n) ×ᵤ c   ≈⟨ U.×-homo-+ c m n ⟩
   m ×ᵤ c + n ×ᵤ c  ≈⟨ +-cong (×ᵤ≈× m c) (×ᵤ≈× n c) ⟩
   m ×  c + n ×  c  ∎
@@ -79,8 +79,8 @@ open import Algebra.Definitions.RawMonoid rawMonoid public
 
 ×-assocˡ : ∀ x m n → m × (n × x) ≈ (m ℕ.* n) × x
 ×-assocˡ x m n = begin
-  m ×  (n ×  x)  ≈˘⟨ ×-congʳ m (×ᵤ≈× n x) ⟩
-  m ×  (n ×ᵤ x)  ≈˘⟨ ×ᵤ≈× m (n ×ᵤ x) ⟩
+  m ×  (n ×  x)  ≈⟨ ×-congʳ m (×ᵤ≈× n x) ⟨
+  m ×  (n ×ᵤ x)  ≈⟨ ×ᵤ≈× m (n ×ᵤ x) ⟨
   m ×ᵤ (n ×ᵤ x)  ≈⟨  U.×-assocˡ x m n ⟩
   (m ℕ.* n) ×ᵤ x ≈⟨  ×ᵤ≈× (m ℕ.* n) x ⟩
   (m ℕ.* n) ×  x ∎
diff --git a/src/Algebra/Properties/Monoid/Sum.agda b/src/Algebra/Properties/Monoid/Sum.agda
index 166cba4462..6ba7d12fc8 100644
--- a/src/Algebra/Properties/Monoid/Sum.agda
+++ b/src/Algebra/Properties/Monoid/Sum.agda
@@ -81,11 +81,11 @@ sum-replicate-zero (suc n) = sum-replicate-idem (+-identityˡ 0#) (suc n)
 sum-init-last : ∀ {n} (t : Vector Carrier (suc n)) → sum t ≈ sum (init t) + last t
 sum-init-last {zero} t  = begin
   t₀ + 0# ≈⟨ +-identityʳ t₀ ⟩
-  t₀      ≈˘⟨ +-identityˡ t₀ ⟩
+  t₀      ≈⟨ +-identityˡ t₀ ⟨
   0# + t₀ ∎ where t₀ = t zero
 sum-init-last {suc n} t = begin
   t₀ + ∑t             ≈⟨ +-congˡ (sum-init-last (tail t)) ⟩
-  t₀ + (∑t′ + tₗ)     ≈˘⟨ +-assoc _ _ _ ⟩
+  t₀ + (∑t′ + tₗ)     ≈⟨ +-assoc _ _ _ ⟨
   (t₀ + ∑t′) + tₗ     ∎
   where
     t₀ = head t
diff --git a/src/Algebra/Properties/Semiring/Binomial.agda b/src/Algebra/Properties/Semiring/Binomial.agda
index 122da9fcb9..6731018af6 100644
--- a/src/Algebra/Properties/Semiring/Binomial.agda
+++ b/src/Algebra/Properties/Semiring/Binomial.agda
@@ -77,7 +77,7 @@ term₂[n,n+1]≈0# n rewrite view-fromℕ (suc n) = refl
 lemma₁ : ∀ n → x * binomialExpansion n ≈ sum₁ n
 lemma₁ n = begin
   x * binomialExpansion n                ≈⟨ *-distribˡ-sum x (binomialTerm n) ⟩
-  ∑[ i ≤ n ] (x * binomialTerm n i)      ≈˘⟨ +-identityˡ _ ⟩
+  ∑[ i ≤ n ] (x * binomialTerm n i)      ≈⟨ +-identityˡ _ ⟨
   0# + ∑[ i ≤ n ] (x * binomialTerm n i) ≡⟨⟩
   0# + ∑[ i ≤ n ] term₁ n (suc i)        ≡⟨⟩
   sum₁ n                                 ∎
@@ -85,9 +85,9 @@ lemma₁ n = begin
 lemma₂ : ∀ n → y * binomialExpansion n ≈ sum₂ n
 lemma₂ n = begin
   y * binomialExpansion n                       ≈⟨ *-distribˡ-sum y (binomialTerm n) ⟩
-  ∑[ i ≤ n ] (y * binomialTerm n i)             ≈˘⟨ +-identityʳ _ ⟩
+  ∑[ i ≤ n ] (y * binomialTerm n i)             ≈⟨ +-identityʳ _ ⟨
   ∑[ i ≤ n ] (y * binomialTerm n i) + 0#        ≈⟨ +-cong (sum-cong-≋ lemma₂-inject₁) (sym (term₂[n,n+1]≈0# n)) ⟩
-  (∑[ i ≤ n ] term₂-inject₁ i) + term₂ n [n+1]  ≈˘⟨ sum-init-last (term₂ n) ⟩
+  (∑[ i ≤ n ] term₂-inject₁ i) + term₂ n [n+1]  ≈⟨ sum-init-last (term₂ n) ⟨
   sum (term₂ n)                                 ≡⟨⟩
   sum₂ n                                        ∎
   where
@@ -106,8 +106,8 @@ x*lemma : ∀ {n} (i : Fin (suc n)) →
           x * binomialTerm n i ≈ (n C toℕ i) × binomial (suc n) (suc i)
 x*lemma {n} i = begin
   x * binomialTerm n i                        ≡⟨⟩
-  x * ((n C k) × (x ^ k * y ^ (n ∸ k)))       ≈˘⟨ *-congˡ (×-assoc-* (n C k) _ _) ⟩
-  x * ((n C k) × x ^ k * y ^ (n ∸ k))         ≈˘⟨ *-assoc x ((n C k) × x ^ k) _ ⟩
+  x * ((n C k) × (x ^ k * y ^ (n ∸ k)))       ≈⟨ *-congˡ (×-assoc-* (n C k) _ _) ⟨
+  x * ((n C k) × x ^ k * y ^ (n ∸ k))         ≈⟨ *-assoc x ((n C k) × x ^ k) _ ⟨
   (x * (n C k) × x ^ k) * y ^ (n ∸ k)         ≈⟨ *-congʳ (×-comm-* (n C k) _ _) ⟩
   (n C k) × x ^ (suc k) * y ^ (n ∸ k)         ≡⟨⟩
   (n C k) × x ^ (suc k) * y ^ (suc n ∸ suc k) ≈⟨ ×-assoc-* (n C k) _ _ ⟩
@@ -125,9 +125,9 @@ y*lemma x*y≈y*x {n} j = begin
   nC[j+1] × (y * binomial n (suc j))
     ≈⟨ ×-congʳ nC[j+1] (y*x^m*y^n≈x^m*y^[n+1] x*y≈y*x [j+1] [n-j-1]) ⟩
   nC[j+1] × (x ^ [j+1] * y ^ [n-j])
-    ≈˘⟨ ×-congʳ nC[j+1] (*-congʳ (^-congʳ x (cong suc k≡j))) ⟩
+    ≈⟨ ×-congʳ nC[j+1] (*-congʳ (^-congʳ x (cong suc k≡j))) ⟨
   nC[j+1] × (x ^ [k+1] * y ^ [n-j])
-    ≈˘⟨ ×-congʳ nC[j+1] (*-congˡ (^-congʳ y [n-k]≡[n-j])) ⟩
+    ≈⟨ ×-congʳ nC[j+1] (*-congˡ (^-congʳ y [n-k]≡[n-j])) ⟨
   nC[j+1] × (x ^ [k+1] * y ^ [n-k])
     ≡⟨⟩
   nC[j+1] × (x ^ [k+1] * y ^ [n+1]-[k+1])
@@ -165,8 +165,8 @@ term₁+term₂≈term x*y≈y*x n 0F = begin
   y * (1 × (1# * y ^ n))       ≈⟨ *-congˡ (+-identityʳ (1# * y ^ n)) ⟩
   y * (1# * y ^ n)             ≈⟨ *-congˡ (*-identityˡ (y ^ n)) ⟩
   y * y ^ n                    ≡⟨⟩
-  y ^ suc n                    ≈˘⟨ *-identityˡ (y ^ suc n) ⟩
-  1# * y ^ suc n               ≈˘⟨ +-identityʳ (1# * y ^ suc n) ⟩
+  y ^ suc n                    ≈⟨ *-identityˡ (y ^ suc n) ⟨
+  1# * y ^ suc n               ≈⟨ +-identityʳ (1# * y ^ suc n) ⟨
   1 × (1# * y ^ suc n)         ≡⟨⟩
   binomialTerm (suc n) 0F      ∎
 
@@ -180,8 +180,8 @@ term₁+term₂≈term x*y≈y*x n (suc i) with view i
     = begin
   x * ((x ^ n * 1#) + 0#) + 0# ≈⟨ +-identityʳ _ ⟩
   x * ((x ^ n * 1#) + 0#)      ≈⟨ *-congˡ (+-identityʳ _) ⟩
-  x * (x ^ n * 1#)             ≈˘⟨ *-assoc _ _ _ ⟩
-  x * x ^ n * 1#               ≈˘⟨ +-identityʳ _ ⟩
+  x * (x ^ n * 1#)             ≈⟨ *-assoc _ _ _ ⟨
+  x * x ^ n * 1#               ≈⟨ +-identityʳ _ ⟨
   1 × (x * x ^ n * 1#)         ∎
 
 ... | ‵inject₁ j
@@ -190,9 +190,9 @@ term₁+term₂≈term x*y≈y*x n (suc i) with view i
   (x * binomialTerm n i) + (y * binomialTerm n (suc j))
     ≈⟨ +-cong (x*lemma i) (y*lemma x*y≈y*x j) ⟩
   (nCk × [x^k+1]*[y^n-k]) + (nC[j+1] × [x^k+1]*[y^n-k])
-    ≈˘⟨ +-congˡ (×-congˡ nC[k+1]≡nC[j+1]) ⟩
+    ≈⟨ +-congˡ (×-congˡ nC[k+1]≡nC[j+1]) ⟨
   (nCk × [x^k+1]*[y^n-k]) + (nC[k+1] × [x^k+1]*[y^n-k])
-    ≈˘⟨ ×-homo-+ [x^k+1]*[y^n-k] nCk nC[k+1] ⟩
+    ≈⟨ ×-homo-+ [x^k+1]*[y^n-k] nCk nC[k+1] ⟨
   (nCk Nat.+ nC[k+1]) × [x^k+1]*[y^n-k]
     ≡⟨ cong (_× [x^k+1]*[y^n-k]) (nCk+nC[k+1]≡[n+1]C[k+1] n k) ⟩
   ((suc n) C (suc k)) × [x^k+1]*[y^n-k]
@@ -216,11 +216,11 @@ term₁+term₂≈term x*y≈y*x n (suc i) with view i
 theorem : x * y ≈ y * x → ∀ n → (x + y) ^ n ≈ binomialExpansion n
 theorem x*y≈y*x zero    = begin
   (x + y) ^ 0                     ≡⟨⟩
-  1#                              ≈˘⟨ 1×-identityʳ 1# ⟩
-  1 × 1#                          ≈˘⟨ *-identityʳ (1 × 1#) ⟩
+  1#                              ≈⟨ 1×-identityʳ 1# ⟨
+  1 × 1#                          ≈⟨ *-identityʳ (1 × 1#) ⟨
   (1 × 1#) * 1#                   ≈⟨ ×-assoc-* 1 1# 1# ⟩
   1 × (1# * 1#)                   ≡⟨⟩
-  1 × (x ^ 0 * y ^ 0)             ≈˘⟨ +-identityʳ _ ⟩
+  1 × (x ^ 0 * y ^ 0)             ≈⟨ +-identityʳ _ ⟨
   1 × (x ^ 0 * y ^ 0) + 0#        ≡⟨⟩
   (0 C 0) × (x ^ 0 * y ^ 0) + 0#  ≡⟨⟩
   binomialExpansion 0             ∎
@@ -229,7 +229,7 @@ theorem x*y≈y*x n+1@(suc n) = begin
   (x + y) * (x + y) ^ n                             ≈⟨ *-congˡ (theorem x*y≈y*x n) ⟩
   (x + y) * binomialExpansion n                     ≈⟨ distribʳ _ _ _ ⟩
   x * binomialExpansion n + y * binomialExpansion n ≈⟨ +-cong (lemma₁ n) (lemma₂ n) ⟩
-  sum₁ n + sum₂ n                                   ≈˘⟨ ∑-distrib-+ (term₁ n) (term₂ n) ⟩
+  sum₁ n + sum₂ n                                   ≈⟨ ∑-distrib-+ (term₁ n) (term₂ n) ⟨
   ∑[ i ≤ n+1 ] (term₁ n i + term₂ n i)              ≈⟨ sum-cong-≋ (term₁+term₂≈term x*y≈y*x n) ⟩
   ∑[ i ≤ n+1 ] binomialTerm n+1 i                   ≡⟨⟩
   binomialExpansion n+1                             ∎
diff --git a/src/Algebra/Properties/Semiring/Exp.agda b/src/Algebra/Properties/Semiring/Exp.agda
index 5da80a99f1..ed8b094520 100644
--- a/src/Algebra/Properties/Semiring/Exp.agda
+++ b/src/Algebra/Properties/Semiring/Exp.agda
@@ -57,16 +57,16 @@ y*x^m*y^n≈x^m*y^[n+1] {x} {y} x*y≈y*x = helper
       y * (x ^ ℕ.zero * y ^ n)  ≡⟨⟩
       y * (1# * y ^ n)          ≈⟨ *-congˡ (*-identityˡ (y ^ n)) ⟩
       y * (y ^ n)               ≡⟨⟩
-      y ^ (suc n)               ≈˘⟨ *-identityˡ (y ^ suc n) ⟩
+      y ^ (suc n)               ≈⟨ *-identityˡ (y ^ suc n) ⟨
       1# * y ^ (suc n)          ≡⟨⟩
       x ^ ℕ.zero * y ^ (suc n)  ∎
     helper (suc m) n = begin
       y * (x ^ suc m * y ^ n)    ≡⟨⟩
       y * ((x * x ^ m) * y ^ n)  ≈⟨ *-congˡ (*-assoc x (x ^ m) (y ^ n)) ⟩
-      y * (x * (x ^ m * y ^ n))  ≈˘⟨ *-assoc y x (x ^ m * y ^ n) ⟩
-      y * x * (x ^ m * y ^ n)    ≈˘⟨ *-congʳ x*y≈y*x ⟩
+      y * (x * (x ^ m * y ^ n))  ≈⟨ *-assoc y x (x ^ m * y ^ n) ⟨
+      y * x * (x ^ m * y ^ n)    ≈⟨ *-congʳ x*y≈y*x ⟨
       x * y * (x ^ m * y ^ n)    ≈⟨ *-assoc x y _ ⟩
       x * (y * (x ^ m * y ^ n))  ≈⟨ *-congˡ (helper m n) ⟩
-      x * (x ^ m * y ^ suc n)    ≈˘⟨ *-assoc x (x ^ m) (y ^ suc n) ⟩
+      x * (x ^ m * y ^ suc n)    ≈⟨ *-assoc x (x ^ m) (y ^ suc n) ⟨
       (x * x ^ m) * y ^ suc n    ≡⟨⟩
       x ^ suc m * y ^ suc n      ∎
diff --git a/src/Algebra/Properties/Semiring/Exp/TailRecursiveOptimised.agda b/src/Algebra/Properties/Semiring/Exp/TailRecursiveOptimised.agda
index d661dde6b1..1ad573866d 100644
--- a/src/Algebra/Properties/Semiring/Exp/TailRecursiveOptimised.agda
+++ b/src/Algebra/Properties/Semiring/Exp/TailRecursiveOptimised.agda
@@ -72,7 +72,7 @@ x^[m+1]≈x*[x^m] x m = x^[m]*[x*y]≈x*x^[m]*y x m 1#
 x^[m+n]≈[x^m]*[x^n] : ∀ x m n → x ^ (m ℕ.+ n) ≈ x ^ m * x ^ n
 x^[m+n]≈[x^m]*[x^n] x m n = begin
   x ^ (m  ℕ.+ n)   ≈⟨ x^[m+n]*y≈x^[m]*x^[n]*y x m n 1# ⟩
-  x ^[ m ]* (x ^ n) ≈˘⟨ x^m*y≈x^[m]*y x m (x ^ n) ⟩
+  x ^[ m ]* (x ^ n) ≈⟨ x^m*y≈x^[m]*y x m (x ^ n) ⟨
   x ^ m * x ^ n    ∎
 
 ^≈^ᵘ : ∀ x m → x ^ m ≈ x ^ᵘ m
diff --git a/src/Algebra/Properties/Semiring/Mult.agda b/src/Algebra/Properties/Semiring/Mult.agda
index 3121e8a8e8..801e4f1966 100644
--- a/src/Algebra/Properties/Semiring/Mult.agda
+++ b/src/Algebra/Properties/Semiring/Mult.agda
@@ -30,8 +30,8 @@ open import Algebra.Properties.Monoid.Mult +-monoid public
 ×1-homo-* (suc m) n = begin
   (n ℕ.+ m ℕ.* n) × 1#                ≈⟨  ×-homo-+ 1# n (m ℕ.* n) ⟩
   n × 1# + (m ℕ.* n) × 1#             ≈⟨  +-congˡ (×1-homo-* m n) ⟩
-  n × 1# + (m × 1#) * (n × 1#)        ≈˘⟨ +-congʳ (*-identityˡ _) ⟩
-  1# * (n × 1#) + (m × 1#) * (n × 1#) ≈˘⟨ distribʳ (n × 1#) 1# (m × 1#) ⟩
+  n × 1# + (m × 1#) * (n × 1#)        ≈⟨ +-congʳ (*-identityˡ _) ⟨
+  1# * (n × 1#) + (m × 1#) * (n × 1#) ≈⟨ distribʳ (n × 1#) 1# (m × 1#) ⟨
   (1# + m × 1#) * (n × 1#)            ∎
 
 -- (1 ×_) is the identity
diff --git a/src/Algebra/Properties/Semiring/Mult/TCOptimised.agda b/src/Algebra/Properties/Semiring/Mult/TCOptimised.agda
index 4ea0e2939b..6f1e538e7d 100644
--- a/src/Algebra/Properties/Semiring/Mult/TCOptimised.agda
+++ b/src/Algebra/Properties/Semiring/Mult/TCOptimised.agda
@@ -30,7 +30,7 @@ open import Algebra.Properties.Monoid.Mult.TCOptimised +-monoid public
 
 ×1-homo-* : ∀ m n → (m ℕ.* n) × 1# ≈ (m × 1#) * (n × 1#)
 ×1-homo-* m n = begin
-  (m ℕ.* n) ×  1#        ≈˘⟨ ×ᵤ≈× (m ℕ.* n) 1# ⟩
+  (m ℕ.* n) ×  1#        ≈⟨ ×ᵤ≈× (m ℕ.* n) 1# ⟨
   (m ℕ.* n) ×ᵤ 1#        ≈⟨  U.×1-homo-* m n ⟩
   (m ×ᵤ 1#) * (n ×ᵤ 1#)  ≈⟨  *-cong (×ᵤ≈× m 1#) (×ᵤ≈× n 1#) ⟩
   (m ×  1#) * (n ×  1#)  ∎
diff --git a/src/Algebra/Solver/Ring/NaturalCoefficients.agda b/src/Algebra/Solver/Ring/NaturalCoefficients.agda
index 6d3ab81b37..0c5f807042 100644
--- a/src/Algebra/Solver/Ring/NaturalCoefficients.agda
+++ b/src/Algebra/Solver/Ring/NaturalCoefficients.agda
@@ -64,7 +64,7 @@ private
     where
     to : m ×ᵤ 1# ≈ n ×ᵤ 1# → m × 1# ≈ n × 1#
     to m≈n = begin
-      m ×  1#  ≈˘⟨ ×ᵤ≈× m 1# ⟩
+      m ×  1#  ≈⟨ ×ᵤ≈× m 1# ⟨
       m ×ᵤ 1#  ≈⟨  m≈n ⟩
       n ×ᵤ 1#  ≈⟨  ×ᵤ≈× n 1# ⟩
       n ×  1#  ∎
diff --git a/src/Codata/Guarded/Stream/Relation/Binary/Pointwise.agda b/src/Codata/Guarded/Stream/Relation/Binary/Pointwise.agda
index 9f573cc711..a4908e851f 100644
--- a/src/Codata/Guarded/Stream/Relation/Binary/Pointwise.agda
+++ b/src/Codata/Guarded/Stream/Relation/Binary/Pointwise.agda
@@ -180,7 +180,7 @@ module pw-Reasoning (S : Setoid a ℓ) where
   run `rs .tail = run (`tail `rs)
 
   infix  1 begin_
-  infixr 2 _↺⟨_⟩_ _↺˘⟨_⟩_ _∼⟨_⟩_ _∼˘⟨_⟩_ _≈⟨_⟩_ _≈˘⟨_⟩_ _≡⟨_⟩_ _≡˘⟨_⟩_ _≡⟨⟩_
+  infixr 2 _↺⟨_⟩_ _↺⟨_⟨_ _∼⟨_⟩_ _∼⟨_⟨_ _≈⟨_⟩_ _≈⟨_⟨_ _≡⟨_⟩_ _≡⟨_⟨_ _≡⟨⟩_
   infix  3 _∎
 
   -- Beginning of a proof
@@ -189,16 +189,41 @@ module pw-Reasoning (S : Setoid a ℓ) where
   (begin `rs) .tail = run (`rs .tail)
 
   pattern _↺⟨_⟩_  as as∼bs bs∼cs = `trans {as = as} (`step as∼bs) bs∼cs
-  pattern _↺˘⟨_⟩_ as bs∼as bs∼cs = `trans {as = as} (`sym (`step bs∼as)) bs∼cs
+  pattern _↺⟨_⟨_ as bs∼as bs∼cs = `trans {as = as} (`sym (`step bs∼as)) bs∼cs
   pattern _∼⟨_⟩_  as as∼bs bs∼cs = `trans {as = as} (`lift as∼bs) bs∼cs
-  pattern _∼˘⟨_⟩_ as bs∼as bs∼cs = `trans {as = as} (`sym (`lift bs∼as)) bs∼cs
+  pattern _∼⟨_⟨_ as bs∼as bs∼cs = `trans {as = as} (`sym (`lift bs∼as)) bs∼cs
   pattern _≈⟨_⟩_  as as∼bs bs∼cs = `trans {as = as} (`bisim as∼bs) bs∼cs
-  pattern _≈˘⟨_⟩_ as bs∼as bs∼cs = `trans {as = as} (`sym (`bisim bs∼as)) bs∼cs
+  pattern _≈⟨_⟨_ as bs∼as bs∼cs = `trans {as = as} (`sym (`bisim bs∼as)) bs∼cs
   pattern _≡⟨_⟩_  as as∼bs bs∼cs = `trans {as = as} (`refl as∼bs) bs∼cs
-  pattern _≡˘⟨_⟩_ as bs∼as bs∼cs = `trans {as = as} (`sym (`refl bs∼as)) bs∼cs
+  pattern _≡⟨_⟨_ as bs∼as bs∼cs = `trans {as = as} (`sym (`refl bs∼as)) bs∼cs
   pattern _≡⟨⟩_   as as∼bs       = `trans {as = as} (`refl P.refl) as∼bs
   pattern _∎      as             = `refl  {as = as} P.refl
 
+
+  -- Deprecated v2.0
+  infixr 2 _↺˘⟨_⟩_ _∼˘⟨_⟩_ _≈˘⟨_⟩_ _≡˘⟨_⟩_
+  pattern _↺˘⟨_⟩_ as bs∼as bs∼cs = `trans {as = as} (`sym (`step bs∼as)) bs∼cs
+  pattern _∼˘⟨_⟩_ as bs∼as bs∼cs = `trans {as = as} (`sym (`lift bs∼as)) bs∼cs
+  pattern _≈˘⟨_⟩_ as bs∼as bs∼cs = `trans {as = as} (`sym (`bisim bs∼as)) bs∼cs
+  pattern _≡˘⟨_⟩_ as bs∼as bs∼cs = `trans {as = as} (`sym (`refl bs∼as)) bs∼cs
+  {-# WARNING_ON_USAGE _↺˘⟨_⟩_
+  "Warning: _↺˘⟨_⟩_ was deprecated in v2.0.
+  Please use _↺⟨_⟨_ instead."
+  #-}
+  {-# WARNING_ON_USAGE _∼˘⟨_⟩_
+  "Warning: _∼˘⟨_⟩_ was deprecated in v2.0.
+  Please use _∼⟨_⟨_ instead."
+  #-}
+  {-# WARNING_ON_USAGE _≈˘⟨_⟩_
+  "Warning: _≈˘⟨_⟩_ was deprecated in v2.0.
+  Please use _≈⟨_⟨_ instead."
+  #-}
+  {-# WARNING_ON_USAGE _≡˘⟨_⟩_
+  "Warning: _≡˘⟨_⟩_ was deprecated in v2.0.
+  Please use _≡⟨_⟨_ instead."
+  #-}
+
+
 module ≈-Reasoning {a} {A : Set a} where
 
   open pw-Reasoning (P.setoid A) public
diff --git a/src/Codata/Sized/Colist/Properties.agda b/src/Codata/Sized/Colist/Properties.agda
index 2ec1564627..a4196bb952 100644
--- a/src/Codata/Sized/Colist/Properties.agda
+++ b/src/Codata/Sized/Colist/Properties.agda
@@ -132,7 +132,7 @@ length-scanl c n (a ∷ as) = suc λ { .force → begin
   length (scanl c (c n a) (as .force))
     ≈⟨ length-scanl c (c n a) (as .force) ⟩
   1 ℕ+ length (as .force)
-    ≈˘⟨ length-∷ a as ⟩
+    ≈⟨ length-∷ a as ⟨
   length (a ∷ as) ∎ } where open coℕᵇ.≈-Reasoning
 
 module _ (cons : C → B → C) (alg : A → Maybe (A × B)) where
@@ -153,7 +153,7 @@ module _ (cons : C → B → C) (alg : A → Maybe (A × B)) where
     (cons nil b ∷ _)
      ≈⟨ Eq.refl ∷ (λ where .force → refl) ⟩
     (cons nil b ∷ _)
-     ≈˘⟨ unfold-just (Maybeₚ.map-just eq) ⟩
+     ≈⟨ unfold-just (Maybeₚ.map-just eq) ⟨
     unfold alg′ (a , nil) ∎ } where open ≈-Reasoning
 
 ------------------------------------------------------------------------
diff --git a/src/Data/Fin/Properties.agda b/src/Data/Fin/Properties.agda
index eb5a7f5011..cdcbeb4e85 100644
--- a/src/Data/Fin/Properties.agda
+++ b/src/Data/Fin/Properties.agda
@@ -607,7 +607,7 @@ join-splitAt zero    n i       = refl
 join-splitAt (suc m) n zero    = refl
 join-splitAt (suc m) n (suc i) = begin
   [ _↑ˡ n , (suc m) ↑ʳ_ ]′ (splitAt (suc m) (suc i)) ≡⟨ [,]-map (splitAt m i) ⟩
-  [ suc ∘ (_↑ˡ n) , suc ∘ (m ↑ʳ_) ]′ (splitAt m i)   ≡˘⟨ [,]-∘ suc (splitAt m i) ⟩
+  [ suc ∘ (_↑ˡ n) , suc ∘ (m ↑ʳ_) ]′ (splitAt m i)   ≡⟨ [,]-∘ suc (splitAt m i) ⟨
   suc ([ _↑ˡ n , m ↑ʳ_ ]′ (splitAt m i))             ≡⟨ cong suc (join-splitAt m n i) ⟩
   suc i                                                         ∎
   where open ≡-Reasoning
@@ -646,13 +646,13 @@ remQuot-combine {suc n} {k} (suc i) j rewrite splitAt-↑ʳ k   (n ℕ.* k) (com
 combine-remQuot : ∀ {n} k (i : Fin (n ℕ.* k)) → uncurry combine (remQuot {n} k i) ≡ i
 combine-remQuot {suc n} k i with splitAt k i in eq
 ... | inj₁ j = begin
-  join k (n ℕ.* k) (inj₁ j)      ≡˘⟨ cong (join k (n ℕ.* k)) eq ⟩
+  join k (n ℕ.* k) (inj₁ j)      ≡⟨ cong (join k (n ℕ.* k)) eq ⟨
   join k (n ℕ.* k) (splitAt k i) ≡⟨ join-splitAt k (n ℕ.* k) i ⟩
   i                              ∎
   where open ≡-Reasoning
 ... | inj₂ j = begin
   k ↑ʳ (uncurry combine (remQuot {n} k j)) ≡⟨ cong (k ↑ʳ_) (combine-remQuot {n} k j) ⟩
-  join k (n ℕ.* k) (inj₂ j)                ≡˘⟨ cong (join k (n ℕ.* k)) eq ⟩
+  join k (n ℕ.* k) (inj₂ j)                ≡⟨ cong (join k (n ℕ.* k)) eq ⟨
   join k (n ℕ.* k) (splitAt k i)           ≡⟨ join-splitAt k (n ℕ.* k) i ⟩
   i                                        ∎
   where open ≡-Reasoning
@@ -662,7 +662,7 @@ toℕ-combine {suc m} {n} i@0F j = begin
   toℕ (combine i j)          ≡⟨⟩
   toℕ (j ↑ˡ (m ℕ.* n))       ≡⟨ toℕ-↑ˡ j (m ℕ.* n) ⟩
   toℕ j                      ≡⟨⟩
-  0 ℕ.+ toℕ j                ≡˘⟨ cong (ℕ._+ toℕ j) (ℕₚ.*-zeroʳ n) ⟩
+  0 ℕ.+ toℕ j                ≡⟨ cong (ℕ._+ toℕ j) (ℕₚ.*-zeroʳ n) ⟨
   n ℕ.* toℕ i ℕ.+ toℕ j      ∎
   where open ≡-Reasoning
 toℕ-combine {suc m} {n} (suc i) j = begin
@@ -683,7 +683,7 @@ combine-monoˡ-< {m} {n} {i} {j} k l i<j = begin-strict
   n ℕ.+ toℕ i ℕ.* n      ≡⟨ ℕₚ.*-comm (suc (toℕ i)) n ⟩
   n ℕ.* suc (toℕ i)      ≤⟨ ℕₚ.*-monoʳ-≤ n (toℕ-mono-< i<j) ⟩
   n ℕ.* toℕ j            ≤⟨ ℕₚ.m≤m+n (n ℕ.* toℕ j) (toℕ l) ⟩
-  n ℕ.* toℕ j ℕ.+ toℕ l  ≡˘⟨ toℕ-combine j l ⟩
+  n ℕ.* toℕ j ℕ.+ toℕ l  ≡⟨ toℕ-combine j l ⟨
   toℕ (combine j l)      ∎
   where open ℕₚ.≤-Reasoning; open +-*-Solver
 
@@ -699,7 +699,7 @@ combine-injectiveʳ : ∀ (i : Fin m) (j : Fin n) (k : Fin m) (l : Fin n) →
 combine-injectiveʳ {m} {n} i j k l cᵢⱼ≡cₖₗ
   with refl ← combine-injectiveˡ i j k l cᵢⱼ≡cₖₗ
   = toℕ-injective (ℕₚ.+-cancelˡ-≡ (n ℕ.* toℕ i) _ _ (begin
-  n ℕ.* toℕ i ℕ.+ toℕ j ≡˘⟨ toℕ-combine i j ⟩
+  n ℕ.* toℕ i ℕ.+ toℕ j ≡⟨ toℕ-combine i j ⟨
   toℕ (combine i j)     ≡⟨ cong toℕ cᵢⱼ≡cₖₗ ⟩
   toℕ (combine i l)     ≡⟨ toℕ-combine i l ⟩
   n ℕ.* toℕ i ℕ.+ toℕ l ∎))
@@ -714,7 +714,7 @@ combine-injective i j k l cᵢⱼ≡cₖₗ =
 combine-surjective : ∀ (i : Fin (m ℕ.* n)) → ∃₂ λ j k → combine j k ≡ i
 combine-surjective {m} {n} i with j , k ← remQuot {m} n i in eq
   = j , k , (begin
-  combine j k                       ≡˘⟨ uncurry (cong₂ combine) (,-injective eq) ⟩
+  combine j k                       ≡⟨ uncurry (cong₂ combine) (,-injective eq) ⟨
   uncurry combine (remQuot {m} n i) ≡⟨ combine-remQuot {m} n i ⟩
   i                                 ∎)
   where open ≡-Reasoning
@@ -1092,7 +1092,7 @@ opposite-suc {n} i = begin
   toℕ (opposite (suc i))     ≡⟨ opposite-prop (suc i) ⟩
   suc n ∸ suc (toℕ (suc i))  ≡⟨⟩
   n ∸ toℕ (suc i)            ≡⟨⟩
-  n ∸ suc (toℕ i)            ≡˘⟨ opposite-prop i ⟩
+  n ∸ suc (toℕ i)            ≡⟨ opposite-prop i ⟨
   toℕ (opposite i)           ∎
   where open ≡-Reasoning
 
diff --git a/src/Data/Fin/Subset/Properties.agda b/src/Data/Fin/Subset/Properties.agda
index 2f7246da6a..6029b9a78c 100644
--- a/src/Data/Fin/Subset/Properties.agda
+++ b/src/Data/Fin/Subset/Properties.agda
@@ -784,7 +784,7 @@ p─q─r≡p─r─q : ∀ (p q r : Subset n) → p ─ q ─ r ≡ p ─ r ─
 p─q─r≡p─r─q p q r = begin
   (p ─ q) ─ r  ≡⟨  p─q─r≡p─q∪r p q r ⟩
   p ─ (q ∪ r)  ≡⟨  cong (p ─_) (∪-comm q r) ⟩
-  p ─ (r ∪ q)  ≡˘⟨ p─q─r≡p─q∪r p r q ⟩
+  p ─ (r ∪ q)  ≡⟨ p─q─r≡p─q∪r p r q ⟨
   (p ─ r) ─ q  ∎
   where open ≡-Reasoning
 
diff --git a/src/Data/Integer/DivMod.agda b/src/Data/Integer/DivMod.agda
index 87bbaabbe7..687570ba1b 100644
--- a/src/Data/Integer/DivMod.agda
+++ b/src/Data/Integer/DivMod.agda
@@ -75,7 +75,7 @@ a≡a%ℕn+[a/ℕn]*n n@(-[1+ _ ]) d with ∣ n ∣ ℕ.% d in eq
 [n/ℕd]*d≤n : ∀ n d .{{_ : ℕ.NonZero d}} → (n /ℕ d) * + d ≤ n
 [n/ℕd]*d≤n n d = let q = n /ℕ d; r = n %ℕ d in begin
   q * + d        ≤⟨  i≤j+i _ (+ r) ⟩
-  + r + q * + d  ≡˘⟨ a≡a%ℕn+[a/ℕn]*n n d ⟩
+  + r + q * + d  ≡⟨ a≡a%ℕn+[a/ℕn]*n n d ⟨
   n              ∎
 
 div-pos-is-/ℕ : ∀ n d .{{_ : ℕ.NonZero d}} →
diff --git a/src/Data/Integer/Properties.agda b/src/Data/Integer/Properties.agda
index 13ed3deab8..43152bceee 100644
--- a/src/Data/Integer/Properties.agda
+++ b/src/Data/Integer/Properties.agda
@@ -371,7 +371,7 @@ module ≤-Reasoning where
     <-≤-trans
     ≤-<-trans
     public
-    hiding (step-≈; step-≈˘)
+    hiding (step-≈; step-≈˘; step-≈-⟩; step-≈-⟨)
 
 ------------------------------------------------------------------------
 -- Properties of Positive/NonPositive/Negative/NonNegative and _≤_/_<_
@@ -403,7 +403,7 @@ neg-involutive +[1+ n ] = refl
 
 neg-injective : - i ≡ - j → i ≡ j
 neg-injective {i} {j} -i≡-j = begin
-  i     ≡˘⟨ neg-involutive i ⟩
+  i     ≡⟨ neg-involutive i ⟨
   - - i ≡⟨  cong -_ -i≡-j ⟩
   - - j ≡⟨  neg-involutive j ⟩
   j     ∎ where open ≡-Reasoning
@@ -541,7 +541,7 @@ signᵢ◃∣i∣≡i -[1+ n ] = refl
 sign-cong : .{{_ : ℕ.NonZero m}} .{{_ : ℕ.NonZero n}} →
             s ◃ m ≡ t ◃ n → s ≡ t
 sign-cong {n@(suc _)} {m@(suc _)} {s} {t} eq = begin
-  s             ≡˘⟨ sign-◃ s n ⟩
+  s             ≡⟨ sign-◃ s n ⟨
   sign (s ◃ n)  ≡⟨  cong sign eq ⟩
   sign (t ◃ m)  ≡⟨  sign-◃ t m ⟩
   t             ∎ where open ≡-Reasoning
@@ -556,7 +556,7 @@ sign-cong′ {s}       {suc m} {t}       {suc n} eq = inj₁ (sign-cong eq)
 
 abs-cong : s ◃ m ≡ t ◃ n → m ≡ n
 abs-cong {s} {m} {t} {n} eq = begin
-  m          ≡˘⟨ abs-◃ s m ⟩
+  m          ≡⟨ abs-◃ s m ⟨
   ∣ s ◃ m ∣  ≡⟨  cong ∣_∣ eq ⟩
   ∣ t ◃ n ∣  ≡⟨  abs-◃ t n ⟩
   n          ∎ where open ≡-Reasoning
@@ -608,7 +608,7 @@ n⊖n≡0 n with n ℕ.<ᵇ n in leq
 ⊖-swap (suc m) (suc n) = begin
   suc m ⊖ suc n     ≡⟨ [1+m]⊖[1+n]≡m⊖n m n ⟩
   m ⊖ n             ≡⟨ ⊖-swap m n ⟩
-  - (n ⊖ m)         ≡˘⟨ cong -_ ([1+m]⊖[1+n]≡m⊖n n m) ⟩
+  - (n ⊖ m)         ≡⟨ cong -_ ([1+m]⊖[1+n]≡m⊖n n m) ⟨
   - (suc n ⊖ suc m) ∎ where open ≡-Reasoning
 
 ⊖-≥ : m ℕ.≥ n → m ⊖ n ≡ + (m ∸ n)
@@ -666,12 +666,12 @@ m-n≡m⊖n (suc m) (suc n) = refl
 -[n⊖m]≡-m+n m n with m ℕ.<ᵇ n | Reflects.invert (ℕ.<ᵇ-reflects-< m n)
 ... | true  | p = begin
   - (- (+ (n ∸ m))) ≡⟨ neg-involutive (+ (n ∸ m)) ⟩
-  + (n ∸ m)         ≡˘⟨ ⊖-≥ (ℕ.≤-trans (ℕ.m≤n+m m 1) p) ⟩
-  n ⊖ m             ≡˘⟨ -m+n≡n⊖m m n ⟩
+  + (n ∸ m)         ≡⟨ ⊖-≥ (ℕ.≤-trans (ℕ.m≤n+m m 1) p) ⟨
+  n ⊖ m             ≡⟨ -m+n≡n⊖m m n ⟨
   - (+ m) + + n     ∎ where open ≡-Reasoning
 ... | false | p = begin
-  - (+ (m ∸ n))     ≡˘⟨ ⊖-≤ (ℕ.≮⇒≥ p) ⟩
-  n ⊖ m             ≡˘⟨ -m+n≡n⊖m m n ⟩
+  - (+ (m ∸ n))     ≡⟨ ⊖-≤ (ℕ.≮⇒≥ p) ⟨
+  n ⊖ m             ≡⟨ -m+n≡n⊖m m n ⟨
   - (+ m) + + n     ∎ where open ≡-Reasoning
 
 ∣m⊖n∣≡∣n⊖m∣ : ∀ m n → ∣ m ⊖ n ∣ ≡ ∣ n ⊖ m ∣
@@ -712,14 +712,14 @@ m⊖1+n<m (suc m) (suc n) = begin-strict
 -1+m<n⊖m (suc m) (suc n) = begin-strict
   -[1+ suc m ]  <⟨ -<- ℕ.≤-refl ⟩
   -[1+ m ]      <⟨ -1+m<n⊖m m n ⟩
-  n ⊖ m         ≡˘⟨ [1+m]⊖[1+n]≡m⊖n n m ⟩
+  n ⊖ m         ≡⟨ [1+m]⊖[1+n]≡m⊖n n m ⟨
   suc n ⊖ suc m ∎ where open ≤-Reasoning
 
 -[1+m]≤n⊖m+1 : ∀ m n → -[1+ m ] ≤ n ⊖ suc m
 -[1+m]≤n⊖m+1 m zero    = ≤-refl
 -[1+m]≤n⊖m+1 m (suc n) = begin
   -[1+ m ]      ≤⟨ <⇒≤ (-1+m<n⊖m m n) ⟩
-  n ⊖ m         ≡˘⟨ [1+m]⊖[1+n]≡m⊖n n m ⟩
+  n ⊖ m         ≡⟨ [1+m]⊖[1+n]≡m⊖n n m ⟨
   suc n ⊖ suc m ∎ where open ≤-Reasoning
 
 -1+m≤n⊖m : ∀ m n → -[1+ m ] ≤ n ⊖ m
@@ -750,7 +750,7 @@ sign-⊖-≰ = sign-⊖-< ∘ ℕ.≰⇒>
 ⊖-monoʳ-≥-≤ (suc n) {suc m} {suc o} (s≤s m≤o) = begin
   suc n ⊖ suc m ≡⟨  [1+m]⊖[1+n]≡m⊖n n m ⟩
   n ⊖ m         ≤⟨  ⊖-monoʳ-≥-≤ n m≤o ⟩
-  n ⊖ o         ≡˘⟨ [1+m]⊖[1+n]≡m⊖n n o ⟩
+  n ⊖ o         ≡⟨ [1+m]⊖[1+n]≡m⊖n n o ⟨
   suc n ⊖ suc o ∎ where open ≤-Reasoning
 
 ⊖-monoˡ-≤ : ∀ n → (_⊖ n) Preserves ℕ._≤_ ⟶ _≤_
@@ -759,12 +759,12 @@ sign-⊖-≰ = sign-⊖-< ∘ ℕ.≰⇒>
 ⊖-monoˡ-≤ (suc n) {_} {suc o} z≤n = begin
   zero ⊖ suc n  ≤⟨  ⊖-monoʳ-≥-≤ 0 (ℕ.n≤1+n n) ⟩
   zero ⊖ n      ≤⟨  ⊖-monoˡ-≤ n z≤n ⟩
-  o ⊖ n         ≡˘⟨ [1+m]⊖[1+n]≡m⊖n o n ⟩
+  o ⊖ n         ≡⟨ [1+m]⊖[1+n]≡m⊖n o n ⟨
   suc o ⊖ suc n ∎ where open ≤-Reasoning
 ⊖-monoˡ-≤ (suc n) {suc m} {suc o} (s≤s m≤o) = begin
   suc m ⊖ suc n ≡⟨  [1+m]⊖[1+n]≡m⊖n m n ⟩
   m ⊖ n         ≤⟨  ⊖-monoˡ-≤ n m≤o ⟩
-  o ⊖ n         ≡˘⟨ [1+m]⊖[1+n]≡m⊖n o n ⟩
+  o ⊖ n         ≡⟨ [1+m]⊖[1+n]≡m⊖n o n ⟨
   suc o ⊖ suc n ∎ where open ≤-Reasoning
 
 ⊖-monoʳ->-< : ∀ p → (p ⊖_) Preserves ℕ._>_ ⟶ _<_
@@ -777,19 +777,19 @@ sign-⊖-≰ = sign-⊖-< ∘ ℕ.≰⇒>
 ⊖-monoʳ->-< (suc p) {suc m} {suc n} (s<s m<n@(s≤s _)) = begin-strict
   suc p ⊖ suc m ≡⟨  [1+m]⊖[1+n]≡m⊖n p m ⟩
   p ⊖ m         <⟨  ⊖-monoʳ->-< p m<n ⟩
-  p ⊖ n         ≡˘⟨ [1+m]⊖[1+n]≡m⊖n p n ⟩
+  p ⊖ n         ≡⟨ [1+m]⊖[1+n]≡m⊖n p n ⟨
   suc p ⊖ suc n ∎ where open ≤-Reasoning
 
 ⊖-monoˡ-< : ∀ n → (_⊖ n) Preserves ℕ._<_ ⟶ _<_
 ⊖-monoˡ-< zero    m<o             = +<+ m<o
 ⊖-monoˡ-< (suc n) {_} {suc o} z<s = begin-strict
   -[1+ n ]      <⟨  -1+m<n⊖m n _ ⟩
-  o ⊖ n         ≡˘⟨ [1+m]⊖[1+n]≡m⊖n o n ⟩
+  o ⊖ n         ≡⟨ [1+m]⊖[1+n]≡m⊖n o n ⟨
   suc o ⊖ suc n ∎ where open ≤-Reasoning
 ⊖-monoˡ-< (suc n) {suc m} {suc (suc o)} (s<s m<o@(s≤s _)) = begin-strict
   suc m ⊖ suc n       ≡⟨  [1+m]⊖[1+n]≡m⊖n m n ⟩
   m ⊖ n               <⟨  ⊖-monoˡ-< n m<o ⟩
-  suc o ⊖ n           ≡˘⟨ [1+m]⊖[1+n]≡m⊖n (suc o) n ⟩
+  suc o ⊖ n           ≡⟨ [1+m]⊖[1+n]≡m⊖n (suc o) n ⟨
   suc (suc o) ⊖ suc n ∎ where open ≤-Reasoning
 
 ------------------------------------------------------------------------
@@ -822,7 +822,7 @@ distribˡ-⊖-+-pos _ (suc _) zero    = refl
 distribˡ-⊖-+-pos m (suc n) (suc o) = begin
   suc n ⊖ suc o + + m   ≡⟨ cong (_+ + m) ([1+m]⊖[1+n]≡m⊖n n o) ⟩
   n ⊖ o + + m           ≡⟨ distribˡ-⊖-+-pos m n o ⟩
-  n ℕ.+ m ⊖ o           ≡˘⟨ [1+m]⊖[1+n]≡m⊖n (n ℕ.+ m) o ⟩
+  n ℕ.+ m ⊖ o           ≡⟨ [1+m]⊖[1+n]≡m⊖n (n ℕ.+ m) o ⟨
   suc (n ℕ.+ m) ⊖ suc o ∎ where open ≡-Reasoning
 
 distribˡ-⊖-+-neg : ∀ m n o → n ⊖ o + -[1+ m ] ≡ n ⊖ (suc o ℕ.+ m)
@@ -832,7 +832,7 @@ distribˡ-⊖-+-neg _ (suc _) zero    = refl
 distribˡ-⊖-+-neg m (suc n) (suc o) = begin
   suc n ⊖ suc o + -[1+ m ]    ≡⟨ cong (_+ -[1+ m ]) ([1+m]⊖[1+n]≡m⊖n n o) ⟩
   n ⊖ o + -[1+ m ]            ≡⟨ distribˡ-⊖-+-neg m n o ⟩
-  n ⊖ (suc o ℕ.+ m)           ≡˘⟨ [1+m]⊖[1+n]≡m⊖n n (suc o ℕ.+ m) ⟩
+  n ⊖ (suc o ℕ.+ m)           ≡⟨ [1+m]⊖[1+n]≡m⊖n n (suc o ℕ.+ m) ⟨
   suc n ⊖ (suc (suc o) ℕ.+ m) ∎ where open ≡-Reasoning
 
 distribʳ-⊖-+-pos : ∀ m n o → + m + (n ⊖ o) ≡ m ℕ.+ n ⊖ o
@@ -855,18 +855,18 @@ distribʳ-⊖-+-neg m n o = begin
 +-assoc i j +0 rewrite +-identityʳ (i + j) | +-identityʳ  j      = refl
 +-assoc -[1+ m ] -[1+ n ] +[1+ o ] = begin
   suc o ⊖ suc (suc (m ℕ.+ n)) ≡⟨ [1+m]⊖[1+n]≡m⊖n o (suc m ℕ.+ n) ⟩
-  o ⊖ (suc m ℕ.+ n)           ≡˘⟨ distribʳ-⊖-+-neg m o n ⟩
-  -[1+ m ] + (o ⊖ n)          ≡˘⟨ cong (λ z → -[1+ m ] + z) ([1+m]⊖[1+n]≡m⊖n o n) ⟩
+  o ⊖ (suc m ℕ.+ n)           ≡⟨ distribʳ-⊖-+-neg m o n ⟨
+  -[1+ m ] + (o ⊖ n)          ≡⟨ cong (λ z → -[1+ m ] + z) ([1+m]⊖[1+n]≡m⊖n o n) ⟨
   -[1+ m ] + (suc o ⊖ suc n)  ∎ where open ≡-Reasoning
 +-assoc -[1+ m ] +[1+ n ] +[1+ o ] = begin
   suc n ⊖ suc m + +[1+ o ]  ≡⟨ cong (_+ +[1+ o ]) ([1+m]⊖[1+n]≡m⊖n n m) ⟩
   (n ⊖ m) + +[1+ o ]        ≡⟨ distribˡ-⊖-+-pos (suc o) n m ⟩
-  n ℕ.+ suc o ⊖ m           ≡˘⟨ [1+m]⊖[1+n]≡m⊖n (n ℕ.+ suc o) m ⟩
+  n ℕ.+ suc o ⊖ m           ≡⟨ [1+m]⊖[1+n]≡m⊖n (n ℕ.+ suc o) m ⟨
   suc (n ℕ.+ suc o) ⊖ suc m ∎ where open ≡-Reasoning
 +-assoc +[1+ m ] -[1+ n ] -[1+ o ] = begin
   (suc m ⊖ suc n) + -[1+ o ]  ≡⟨ cong (_+ -[1+ o ]) ([1+m]⊖[1+n]≡m⊖n m n) ⟩
   (m ⊖ n) + -[1+ o ]          ≡⟨ distribˡ-⊖-+-neg o m n ⟩
-  m ⊖ suc (n ℕ.+ o)           ≡˘⟨ [1+m]⊖[1+n]≡m⊖n m (suc n ℕ.+ o) ⟩
+  m ⊖ suc (n ℕ.+ o)           ≡⟨ [1+m]⊖[1+n]≡m⊖n m (suc n ℕ.+ o) ⟨
   suc m ⊖ suc (suc (n ℕ.+ o)) ∎ where open ≡-Reasoning
 +-assoc +[1+ m ] -[1+ n ] +[1+ o ]
   rewrite [1+m]⊖[1+n]≡m⊖n m n
@@ -1087,8 +1087,8 @@ neg-minus-pos (suc m) (suc n) = cong (-[1+_] ∘ suc) (ℕ.+-comm (suc m) n)
 +-minus-telescope : ∀ i j k → (i - j) + (j - k) ≡ i - k
 +-minus-telescope i j k = begin
   (i - j) + (j - k)   ≡⟨  +-assoc i (- j) (j - k) ⟩
-  i + (- j + (j - k)) ≡˘⟨ cong (λ v → i + v) (+-assoc (- j) j _) ⟩
-  i + ((- j + j) - k) ≡˘⟨ +-assoc i (- j + j) (- k) ⟩
+  i + (- j + (j - k)) ≡⟨ cong (λ v → i + v) (+-assoc (- j) j _) ⟨
+  i + ((- j + j) - k) ≡⟨ +-assoc i (- j + j) (- k) ⟨
   i + (- j + j) - k   ≡⟨  cong (λ a → i + a - k) (+-inverseˡ j) ⟩
   i + 0ℤ - k          ≡⟨  cong (_- k) (+-identityʳ i) ⟩
   i - k               ∎ where open ≡-Reasoning
@@ -1103,16 +1103,16 @@ neg-minus-pos (suc m) (suc n) = cong (-[1+_] ∘ suc) (ℕ.+-comm (suc m) n)
 ∣i-j∣≡∣j-i∣ -[1+ m ] -[1+ n ] = ∣m⊖n∣≡∣n⊖m∣ (suc n) (suc m)
 ∣i-j∣≡∣j-i∣ -[1+ m ] (+ n)    = begin
   ∣ -[1+ m ] - (+ n) ∣  ≡⟨  cong ∣_∣ (neg-minus-pos m n) ⟩
-  suc (n ℕ.+ m)         ≡˘⟨ ℕ.+-suc n m ⟩
+  suc (n ℕ.+ m)         ≡⟨ ℕ.+-suc n m ⟨
   n ℕ.+ suc m           ∎ where open ≡-Reasoning
 ∣i-j∣≡∣j-i∣ (+ m) -[1+ n ] = begin
   m ℕ.+ suc n          ≡⟨  ℕ.+-suc m n ⟩
-  suc (m ℕ.+ n)        ≡˘⟨ cong ∣_∣ (neg-minus-pos n m) ⟩
+  suc (m ℕ.+ n)        ≡⟨ cong ∣_∣ (neg-minus-pos n m) ⟨
   ∣ -[1+ n ] + - + m ∣ ∎ where open ≡-Reasoning
 ∣i-j∣≡∣j-i∣ (+ m) (+ n) = begin
   ∣ + m - + n ∣  ≡⟨  cong ∣_∣ ([+m]-[+n]≡m⊖n m n) ⟩
   ∣ m ⊖ n ∣      ≡⟨  ∣m⊖n∣≡∣n⊖m∣ m n ⟩
-  ∣ n ⊖ m ∣      ≡˘⟨ cong ∣_∣ ([+m]-[+n]≡m⊖n n m) ⟩
+  ∣ n ⊖ m ∣      ≡⟨ cong ∣_∣ ([+m]-[+n]≡m⊖n n m) ⟨
   ∣ + n - + m ∣  ∎ where open ≡-Reasoning
 
 ∣-∣-≤ : i ≤ j → + ∣ i - j ∣ ≡ j - i
@@ -1140,9 +1140,9 @@ i≡j⇒i-j≡0 {i} refl = +-inverseʳ i
 
 i-j≡0⇒i≡j : ∀ i j → i - j ≡ 0ℤ → i ≡ j
 i-j≡0⇒i≡j i j i-j≡0 = begin
-  i             ≡˘⟨ +-identityʳ i ⟩
-  i + 0ℤ        ≡˘⟨ cong (_+_ i) (+-inverseˡ j) ⟩
-  i + (- j + j) ≡˘⟨ +-assoc i (- j) j ⟩
+  i             ≡⟨ +-identityʳ i ⟨
+  i + 0ℤ        ≡⟨ cong (_+_ i) (+-inverseˡ j) ⟨
+  i + (- j + j) ≡⟨ +-assoc i (- j) j ⟨
   (i - j) + j   ≡⟨  cong (_+ j) i-j≡0 ⟩
   0ℤ + j        ≡⟨  +-identityˡ j ⟩
   j             ∎ where open ≡-Reasoning
@@ -1172,9 +1172,9 @@ i≤j⇒i-j≤0 {+[1+ m ]} {+[1+ n ]} (+≤+ (s≤s m≤n)) = begin
 
 i-j≤0⇒i≤j : i - j ≤ 0ℤ → i ≤ j
 i-j≤0⇒i≤j {i} {j} i-j≤0 = begin
-  i             ≡˘⟨ +-identityʳ i ⟩
-  i + 0ℤ        ≡˘⟨ cong (_+_ i) (+-inverseˡ j) ⟩
-  i + (- j + j) ≡˘⟨ +-assoc i (- j) j ⟩
+  i             ≡⟨ +-identityʳ i ⟨
+  i + 0ℤ        ≡⟨ cong (_+_ i) (+-inverseˡ j) ⟨
+  i + (- j + j) ≡⟨ +-assoc i (- j) j ⟨
   (i - j) + j   ≤⟨  +-monoˡ-≤ j i-j≤0 ⟩
   0ℤ + j        ≡⟨  +-identityˡ j ⟩
   j             ∎
@@ -1182,14 +1182,14 @@ i-j≤0⇒i≤j {i} {j} i-j≤0 = begin
 
 i≤j⇒0≤j-i : i ≤ j → 0ℤ ≤ j - i
 i≤j⇒0≤j-i {i} {j} i≤j = begin
-  0ℤ    ≡˘⟨ +-inverseʳ i ⟩
+  0ℤ    ≡⟨ +-inverseʳ i ⟨
   i - i ≤⟨  +-monoˡ-≤ (- i) i≤j ⟩
   j - i ∎
   where open ≤-Reasoning
 
 0≤i-j⇒j≤i : 0ℤ ≤ i - j → j ≤ i
 0≤i-j⇒j≤i {i} {j} 0≤i-j = begin
-  j             ≡˘⟨ +-identityˡ j ⟩
+  j             ≡⟨ +-identityˡ j ⟨
   0ℤ + j        ≤⟨  +-monoˡ-≤ j 0≤i-j ⟩
   i - j + j     ≡⟨  +-assoc i (- j) j ⟩
   i + (- j + j) ≡⟨  cong (_+_ i) (+-inverseˡ j) ⟩
@@ -1246,19 +1246,19 @@ i<j⇒suc[i]≤j { -[1+ suc i ]} {+ _}       -<+       = -≤+
 
 suc-pred : ∀ i → sucℤ (pred i) ≡ i
 suc-pred i = begin
-  sucℤ (pred i) ≡˘⟨ +-assoc 1ℤ -1ℤ i ⟩
+  sucℤ (pred i) ≡⟨ +-assoc 1ℤ -1ℤ i ⟨
   0ℤ + i        ≡⟨  +-identityˡ i ⟩
   i             ∎ where open ≡-Reasoning
 
 pred-suc : ∀ i → pred (sucℤ i) ≡ i
 pred-suc i = begin
-  pred (sucℤ i) ≡˘⟨ +-assoc -1ℤ 1ℤ i ⟩
+  pred (sucℤ i) ≡⟨ +-assoc -1ℤ 1ℤ i ⟨
   0ℤ + i        ≡⟨  +-identityˡ i ⟩
   i             ∎ where open ≡-Reasoning
 
 +-pred : ∀ i j → i + pred j ≡ pred (i + j)
 +-pred i j = begin
-  i + (-1ℤ + j) ≡˘⟨ +-assoc i -1ℤ j ⟩
+  i + (-1ℤ + j) ≡⟨ +-assoc i -1ℤ j ⟨
   i + -1ℤ + j   ≡⟨  cong (_+ j) (+-comm i -1ℤ) ⟩
   -1ℤ + i + j   ≡⟨  +-assoc -1ℤ i j ⟩
   -1ℤ + (i + j) ∎ where open ≡-Reasoning
@@ -1419,12 +1419,12 @@ private
 *-distribʳ-+ -[1+ m ] -[1+ n ] +[1+ o ] = begin
   (suc o ⊖ suc n) * -[1+ m ]                ≡⟨ cong (_* -[1+ m ]) ([1+m]⊖[1+n]≡m⊖n o n) ⟩
   (o ⊖ n) * -[1+ m ]                        ≡⟨ distrib-lemma m n o ⟩
-  m ℕ.+ n ℕ.* suc m ⊖ (m ℕ.+ o ℕ.* suc m)   ≡˘⟨ [1+m]⊖[1+n]≡m⊖n (m ℕ.+ n ℕ.* suc m) (m ℕ.+ o ℕ.* suc m) ⟩
+  m ℕ.+ n ℕ.* suc m ⊖ (m ℕ.+ o ℕ.* suc m)   ≡⟨ [1+m]⊖[1+n]≡m⊖n (m ℕ.+ n ℕ.* suc m) (m ℕ.+ o ℕ.* suc m) ⟨
   -[1+ n ] * -[1+ m ] + +[1+ o ] * -[1+ m ] ∎ where open ≡-Reasoning
 *-distribʳ-+ -[1+ m ] +[1+ n ] -[1+ o ] = begin
   (+[1+ n ] + -[1+ o ]) * -[1+ m ]          ≡⟨ cong (_* -[1+ m ]) ([1+m]⊖[1+n]≡m⊖n n o) ⟩
   (n ⊖ o) * -[1+ m ]                        ≡⟨ distrib-lemma m o n ⟩
-  m ℕ.+ o ℕ.* suc m ⊖ (m ℕ.+ n ℕ.* suc m)   ≡˘⟨ [1+m]⊖[1+n]≡m⊖n (m ℕ.+ o ℕ.* suc m) (m ℕ.+ n ℕ.* suc m) ⟩
+  m ℕ.+ o ℕ.* suc m ⊖ (m ℕ.+ n ℕ.* suc m)   ≡⟨ [1+m]⊖[1+n]≡m⊖n (m ℕ.+ o ℕ.* suc m) (m ℕ.+ n ℕ.* suc m) ⟨
   +[1+ n ] * -[1+ m ] + -[1+ o ] * -[1+ m ] ∎ where open ≡-Reasoning
 *-distribʳ-+ +[1+ m ] -[1+ n ] +[1+ o ] with n ℕ.≤? o
 ... | yes n≤o
@@ -1690,8 +1690,8 @@ pos-* (suc m) (suc n) = refl
 
 neg-distribˡ-* : ∀ i j → - (i * j) ≡ (- i) * j
 neg-distribˡ-* i j = begin
-  - (i * j)      ≡˘⟨ -1*i≡-i (i * j) ⟩
-  -1ℤ * (i * j)  ≡˘⟨ *-assoc -1ℤ i j ⟩
+  - (i * j)      ≡⟨ -1*i≡-i (i * j) ⟨
+  -1ℤ * (i * j)  ≡⟨ *-assoc -1ℤ i j ⟨
   -1ℤ * i * j    ≡⟨ cong (_* j) (-1*i≡-i i) ⟩
   - i * j        ∎ where open ≡-Reasoning
 
@@ -1747,10 +1747,10 @@ neg-distribʳ-* i j = begin
 
 *-cancelˡ-≤-neg : ∀ i j k .{{_ : Negative i}} → i * j ≤ i * k → j ≥ k
 *-cancelˡ-≤-neg i@(-[1+ _ ]) j k ij≤ik = neg-cancel-≤ (*-cancelˡ-≤-pos (- j) (- k) (- i) (begin
-  - i * - j   ≡˘⟨ neg-distribʳ-* (- i) j ⟩
+  - i * - j   ≡⟨ neg-distribʳ-* (- i) j ⟨
   -(- i * j)  ≡⟨  neg-distribˡ-* (- i) j ⟩
   i * j       ≤⟨  ij≤ik ⟩
-  i * k       ≡˘⟨ neg-distribˡ-* (- i) k ⟩
+  i * k       ≡⟨ neg-distribˡ-* (- i) k ⟨
   -(- i * k)  ≡⟨  neg-distribʳ-* (- i) k ⟩
   - i * - k   ∎))
   where open ≤-Reasoning
@@ -1761,10 +1761,10 @@ neg-distribʳ-* i j = begin
 *-monoˡ-≤-nonPos : ∀ i .{{_ : NonPositive i}} → (i *_) Preserves _≤_ ⟶ _≥_
 *-monoˡ-≤-nonPos +0           {j} {k} j≤k = +≤+ z≤n
 *-monoˡ-≤-nonPos i@(-[1+ m ]) {j} {k} j≤k = begin
-  i * k        ≡˘⟨ neg-distribˡ-* (- i) k ⟩
+  i * k        ≡⟨ neg-distribˡ-* (- i) k ⟨
   -(- i * k)   ≡⟨  neg-distribʳ-* (- i) k ⟩
   - i * - k    ≤⟨  *-monoˡ-≤-nonNeg (- i) (neg-mono-≤ j≤k) ⟩
-  - i * - j    ≡˘⟨ neg-distribʳ-* (- i) j ⟩
+  - i * - j    ≡⟨ neg-distribʳ-* (- i) j ⟨
   -(- i * j)   ≡⟨  neg-distribˡ-* (- i) j ⟩
   i * j        ∎
   where open ≤-Reasoning
@@ -1794,10 +1794,10 @@ neg-distribʳ-* i j = begin
 
 *-monoˡ-<-neg : ∀ i .{{_ : Negative i}} → (i *_) Preserves _<_ ⟶ _>_
 *-monoˡ-<-neg i@(-[1+ _ ]) {j} {k} j<k = begin-strict
-  i * k        ≡˘⟨ neg-distribˡ-* (- i) k ⟩
+  i * k        ≡⟨ neg-distribˡ-* (- i) k ⟨
   -(- i * k)   ≡⟨  neg-distribʳ-* (- i) k ⟩
   - i * - k    <⟨  *-monoˡ-<-pos (- i) (neg-mono-< j<k) ⟩
-  - i * - j    ≡˘⟨ neg-distribʳ-* (- i) j ⟩
+  - i * - j    ≡⟨ neg-distribʳ-* (- i) j ⟨
   - (- i * j)  ≡⟨  neg-distribˡ-* (- i) j ⟩
   i * j        ∎
   where open ≤-Reasoning
@@ -1808,10 +1808,10 @@ neg-distribʳ-* i j = begin
 *-cancelˡ-<-nonPos : ∀ k .{{_ : NonPositive k}} → k * i < k * j → i > j
 *-cancelˡ-<-nonPos {i} {j} +0           (+<+ ())
 *-cancelˡ-<-nonPos {i} {j} k@(-[1+ _ ]) ki<kj = neg-cancel-< (*-cancelˡ-<-nonNeg (- k) (begin-strict
-  - k * - i   ≡˘⟨ neg-distribʳ-* (- k) i ⟩
+  - k * - i   ≡⟨ neg-distribʳ-* (- k) i ⟨
   -(- k * i)  ≡⟨  neg-distribˡ-* (- k) i ⟩
   k * i       <⟨  ki<kj ⟩
-  k * j       ≡˘⟨ neg-distribˡ-* (- k) j ⟩
+  k * j       ≡⟨ neg-distribˡ-* (- k) j ⟨
   -(- k * j)  ≡⟨  neg-distribʳ-* (- k) j ⟩
   - k * - j   ∎))
   where open ≤-Reasoning
diff --git a/src/Data/List/Effectful.agda b/src/Data/List/Effectful.agda
index 3d4e557468..b21ddf7616 100644
--- a/src/Data/List/Effectful.agda
+++ b/src/Data/List/Effectful.agda
@@ -209,7 +209,7 @@ module Applicative where
              (fs ⊛ as) ≡ (fs >>= pam as)
   unfold-⊛ fs as = begin
     fs ⊛ as
-      ≡˘⟨ concatMap-cong (λ f → P.cong (map f) (concatMap-pure as)) fs ⟩
+      ≡⟨ concatMap-cong (λ f → P.cong (map f) (concatMap-pure as)) fs ⟨
     concatMap (λ f → map f (concatMap pure as)) fs
       ≡⟨ concatMap-cong (λ f → map-concatMap f pure as) fs ⟩
     concatMap (λ f → concatMap (λ x → pure (f x)) as) fs
@@ -224,7 +224,7 @@ module Applicative where
   right-distributive fs₁ fs₂ xs = begin
     (fs₁ ∣ fs₂) ⊛ xs                     ≡⟨ unfold-⊛ (fs₁ ∣ fs₂) xs ⟩
     (fs₁ ∣ fs₂ >>= pam xs)               ≡⟨ MonadProperties.right-distributive fs₁ fs₂ (pam xs) ⟩
-    (fs₁ >>= pam xs) ∣ (fs₂ >>= pam xs)  ≡˘⟨ P.cong₂ _∣_ (unfold-⊛ fs₁ xs) (unfold-⊛ fs₂ xs) ⟩
+    (fs₁ >>= pam xs) ∣ (fs₂ >>= pam xs)  ≡⟨ P.cong₂ _∣_ (unfold-⊛ fs₁ xs) (unfold-⊛ fs₂ xs) ⟨
     (fs₁ ⊛ xs ∣ fs₂ ⊛ xs)                ∎
 
   -- _⊛_ does not distribute over _∣_ from the left.
@@ -251,7 +251,7 @@ module Applicative where
                 (xs : List A) (f : A → B) (fs : B → List C) →
                 (pam xs f >>= fs) ≡ (xs >>= λ x → fs (f x))
     pam-lemma xs f fs = begin
-      (pam xs f >>= fs)                 ≡˘⟨ MP.associative xs (pure ∘ f) fs ⟩
+      (pam xs f >>= fs)                 ≡⟨ MP.associative xs (pure ∘ f) fs ⟨
       (xs >>= λ x → pure (f x) >>= fs)  ≡⟨ MP.cong (refl {x = xs}) (λ x → MP.left-identity (f x) fs) ⟩
       (xs >>= λ x → fs (f x))           ∎
 
@@ -272,7 +272,7 @@ module Applicative where
     (pam fs _∘′_ >>= pam gs >>= pam xs)
       ≡⟨ MP.cong (pam-lemma fs _∘′_ (pam gs)) (λ _ → refl) ⟩
     ((fs >>= λ f → pam gs (f ∘′_)) >>= pam xs)
-      ≡˘⟨ MP.associative fs (λ f → pam gs (_∘′_ f)) (pam xs) ⟩
+      ≡⟨ MP.associative fs (λ f → pam gs (_∘′_ f)) (pam xs) ⟨
     (fs >>= λ f → pam gs (f ∘′_) >>= pam xs)
       ≡⟨ MP.cong (refl {x = fs}) (λ f → pam-lemma gs (f ∘′_) (pam xs)) ⟩
     (fs >>= λ f → gs >>= λ g → pam xs (f ∘′ g))
@@ -282,9 +282,9 @@ module Applicative where
     (fs >>= λ f → gs >>= λ g → pam (pam xs g) f)
       ≡⟨ MP.cong (refl {x = fs}) (λ f → MP.associative gs (pam xs) (pure ∘ f)) ⟩
     (fs >>= pam (gs >>= pam xs))
-      ≡˘⟨ unfold-⊛ fs (gs >>= pam xs) ⟩
+      ≡⟨ unfold-⊛ fs (gs >>= pam xs) ⟨
     fs ⊛ (gs >>= pam xs)
-      ≡˘⟨ P.cong (fs ⊛_) (unfold-⊛ gs xs) ⟩
+      ≡⟨ P.cong (fs ⊛_) (unfold-⊛ gs xs) ⟨
     fs ⊛ (gs ⊛ xs)
       ∎
 
@@ -304,5 +304,5 @@ module Applicative where
                                       MP.left-identity x (pure ∘ f)) ⟩
     (fs >>= λ f → pure (f x))  ≡⟨⟩
     (pam fs (_$′ x))           ≡⟨ P.sym $ MP.left-identity (_$′ x) (pam fs) ⟩
-    (pure (_$′ x) >>= pam fs)  ≡˘⟨ unfold-⊛ (pure (_$′ x)) fs ⟩
+    (pure (_$′ x) >>= pam fs)  ≡⟨ unfold-⊛ (pure (_$′ x)) fs ⟨
     pure (_$′ x) ⊛ fs          ∎
diff --git a/src/Data/List/Properties.agda b/src/Data/List/Properties.agda
index 78fc03f865..5bd47dc763 100644
--- a/src/Data/List/Properties.agda
+++ b/src/Data/List/Properties.agda
@@ -280,7 +280,7 @@ module _ (f : A → B → C) where
   cartesianProductWith-distribʳ-++ (x ∷ xs) ys zs = begin
     prod (x ∷ xs ++ ys) zs ≡⟨⟩
     map (f x) zs ++ prod (xs ++ ys) zs ≡⟨ cong (map (f x) zs ++_) (cartesianProductWith-distribʳ-++ xs ys zs) ⟩
-    map (f x) zs ++ prod xs zs ++ prod ys zs ≡˘⟨ ++-assoc (map (f x) zs) (prod xs zs) (prod ys zs) ⟩
+    map (f x) zs ++ prod xs zs ++ prod ys zs ≡⟨ ++-assoc (map (f x) zs) (prod xs zs) (prod ys zs) ⟨
     (map (f x) zs ++ prod xs zs) ++ prod ys zs ≡⟨⟩
     prod (x ∷ xs) zs ++ prod ys zs ∎
 
@@ -590,7 +590,7 @@ map-concatMap f g xs = begin
   map f (concatMap g xs)
     ≡⟨⟩
   map f (concat (map g xs))
-    ≡˘⟨ concat-map (map g xs) ⟩
+    ≡⟨ concat-map (map g xs) ⟨
   concat (map (map f) (map g xs))
     ≡⟨ cong concat
          {x = map (map f) (map g xs)}
diff --git a/src/Data/List/Relation/Binary/BagAndSetEquality.agda b/src/Data/List/Relation/Binary/BagAndSetEquality.agda
index f842ae8087..31ab6941ac 100644
--- a/src/Data/List/Relation/Binary/BagAndSetEquality.agda
+++ b/src/Data/List/Relation/Binary/BagAndSetEquality.agda
@@ -96,7 +96,7 @@ module ⊆-Reasoning {A : Set a} where
   private module Base = PreorderReasoning (⊆-preorder A)
 
   open Base public
-    hiding (step-≈; step-≈˘; step-∼; step-≲)
+    hiding (step-≈; step-≈˘; step-≈-⟩; step-≈-⟨; step-∼; step-≲)
     renaming (≲-go to ⊆-go)
 
   open begin-membership-syntax _IsRelatedTo_ _∈_ (λ x → begin x) public
@@ -199,7 +199,7 @@ module _ {k} {A B : Set a} {fs gs : List (A → B)} {xs ys} where
     x ∈ (fs >>= λ f → xs >>= λ x → pure (f x))
       ∼⟨ >>=-cong fs≈gs (λ f → >>=-cong xs≈ys λ x → K-refl) ⟩
     x ∈ (gs >>= λ g → ys >>= λ y → pure (g y))
-      ≡˘⟨ P.cong (x ∈_) (Applicative.unfold-⊛ gs ys) ⟩
+      ≡⟨ P.cong (x ∈_) (Applicative.unfold-⊛ gs ys) ⟨
     x ∈ (gs ⊛ ys) ∎
     where open Related.EquationalReasoning
 
@@ -284,7 +284,7 @@ empty-unique {xs = _ ∷ _} ∷∼[] with ⇒→ ∷∼[] (here refl)
                 (xs₂ >>= pure ∘ f))       ≈⟨ >>=-left-distributive fs ⟩
 
   (fs >>= λ f → xs₁ >>= pure ∘ f) ++
-  (fs >>= λ f → xs₂ >>= pure ∘ f)         ≡˘⟨ P.cong₂ _++_ (Applicative.unfold-⊛ fs xs₁) (Applicative.unfold-⊛ fs xs₂) ⟩
+  (fs >>= λ f → xs₂ >>= pure ∘ f)         ≡⟨ P.cong₂ _++_ (Applicative.unfold-⊛ fs xs₁) (Applicative.unfold-⊛ fs xs₂) ⟨
 
   (fs ⊛ xs₁) ++ (fs ⊛ xs₂)                ∎
   where open EqR ([ bag ]-Equality B)
@@ -592,7 +592,7 @@ drop-cons {x = x} {xs} {ys} x∷xs≈x∷ys =
 ... | zs₁ , zs₂ , p rewrite p = begin
   x ∷ xs           <⟨ ∼bag⇒↭ (drop-cons (↔-trans eq (comm zs₁ (x ∷ zs₂)))) ⟩
   x ∷ (zs₂ ++ zs₁) <⟨ ++-comm zs₂ zs₁ ⟩
-  x ∷ (zs₁ ++ zs₂) ↭˘⟨ shift x zs₁ zs₂ ⟩
+  x ∷ (zs₁ ++ zs₂) ↭⟨ shift x zs₁ zs₂ ⟨
   zs₁ ++ x ∷ zs₂   ∎
   where
   open CommutativeMonoid (commutativeMonoid bag A)
diff --git a/src/Data/List/Relation/Binary/Permutation/Propositional.agda b/src/Data/List/Relation/Binary/Permutation/Propositional.agda
index 28cf25d9ed..c41793d28a 100644
--- a/src/Data/List/Relation/Binary/Permutation/Propositional.agda
+++ b/src/Data/List/Relation/Binary/Permutation/Propositional.agda
@@ -76,9 +76,11 @@ module PermutationReasoning where
 
   private module Base = EqReasoning ↭-setoid
 
-  open Base public hiding (step-≈; step-≈˘)
+  open Base public
+    hiding (step-≈; step-≈˘; step-≈-⟩; step-≈-⟨)
+    renaming (≈-go to ↭-go)
 
-  open ↭-syntax _IsRelatedTo_ _IsRelatedTo_ Base.∼-go ↭-sym public
+  open ↭-syntax _IsRelatedTo_ _IsRelatedTo_ ↭-go ↭-sym public
 
   -- Some extra combinators that allow us to skip certain elements
 
diff --git a/src/Data/List/Relation/Binary/Permutation/Propositional/Properties.agda b/src/Data/List/Relation/Binary/Permutation/Propositional/Properties.agda
index 1b33a771a0..781de1cc36 100644
--- a/src/Data/List/Relation/Binary/Permutation/Propositional/Properties.agda
+++ b/src/Data/List/Relation/Binary/Permutation/Propositional/Properties.agda
@@ -243,7 +243,7 @@ drop-mid {A = A} {x} ws xs p = drop-mid′ p ws xs refl refl
 ++-comm []       ys = ↭-sym (++-identityʳ ys)
 ++-comm (x ∷ xs) ys = begin
   x ∷ xs ++ ys   <⟨ ++-comm xs ys ⟩
-  x ∷ ys ++ xs   ↭˘⟨ shift x ys xs ⟩
+  x ∷ ys ++ xs   ↭⟨ shift x ys xs ⟨
   ys ++ (x ∷ xs) ∎
 
 ++-isMagma : IsMagma {A = List A} _↭_ _++_
@@ -296,7 +296,7 @@ module _ {a} {A : Set a} where
 
 shifts : ∀ xs ys {zs : List A} → xs ++ ys ++ zs ↭ ys ++ xs ++ zs
 shifts xs ys {zs} = begin
-   xs ++ ys  ++ zs ↭˘⟨ ++-assoc xs ys zs ⟩
+   xs ++ ys  ++ zs ↭⟨ ++-assoc xs ys zs ⟨
   (xs ++ ys) ++ zs ↭⟨ ++⁺ʳ zs (++-comm xs ys) ⟩
   (ys ++ xs) ++ zs ↭⟨ ++-assoc ys xs zs ⟩
    ys ++ xs  ++ zs ∎
@@ -330,7 +330,7 @@ drop-∷ = drop-mid [] []
 ↭-reverse [] = ↭-refl
 ↭-reverse (x ∷ xs) = begin
   reverse (x ∷ xs) ≡⟨ Lₚ.unfold-reverse x xs ⟩
-  reverse xs ∷ʳ x ↭˘⟨ ∷↭∷ʳ x (reverse xs) ⟩
+  reverse xs ∷ʳ x ↭⟨ ∷↭∷ʳ x (reverse xs) ⟨
   x ∷ reverse xs   ↭⟨ prep x (↭-reverse xs) ⟩
   x ∷ xs ∎
   where open PermutationReasoning
@@ -349,7 +349,7 @@ module _ {ℓ} {R : Rel A ℓ} (R? : Decidable R) where
   ... | true  | rec | _   = prep x rec
   ... | false | _   | rec = begin
     y ∷ merge R? (x ∷ xs) ys <⟨ rec ⟩
-    y ∷ x ∷ xs ++ ys         ↭˘⟨ shift y (x ∷ xs) ys ⟩
-    (x ∷ xs) ++ y ∷ ys       ≡˘⟨ Lₚ.++-assoc [ x ] xs (y ∷ ys) ⟩
+    y ∷ x ∷ xs ++ ys         ↭⟨ shift y (x ∷ xs) ys ⟨
+    (x ∷ xs) ++ y ∷ ys       ≡⟨ Lₚ.++-assoc [ x ] xs (y ∷ ys) ⟨
     x ∷ xs ++ y ∷ ys         ∎
     where open PermutationReasoning
diff --git a/src/Data/List/Relation/Binary/Permutation/Setoid.agda b/src/Data/List/Relation/Binary/Permutation/Setoid.agda
index 0d375226db..edcf62b6da 100644
--- a/src/Data/List/Relation/Binary/Permutation/Setoid.agda
+++ b/src/Data/List/Relation/Binary/Permutation/Setoid.agda
@@ -90,10 +90,12 @@ module PermutationReasoning where
 
   private module Base = SetoidReasoning ↭-setoid
 
-  open Base public hiding (step-≈; step-≈˘)
+  open Base public
+    hiding (step-≈; step-≈˘; step-≈-⟩; step-≈-⟨)
+    renaming (≈-go to ↭-go)
 
-  open ↭-syntax _IsRelatedTo_ _IsRelatedTo_ Base.∼-go ↭-sym public
-  open ≋-syntax _IsRelatedTo_ _IsRelatedTo_ (Base.∼-go ∘′ refl) ≋-sym public
+  open ↭-syntax _IsRelatedTo_ _IsRelatedTo_ ↭-go ↭-sym public
+  open ≋-syntax _IsRelatedTo_ _IsRelatedTo_ (↭-go ∘′ refl) ≋-sym public
 
   -- Some extra combinators that allow us to skip certain elements
 
diff --git a/src/Data/List/Relation/Binary/Permutation/Setoid/Properties.agda b/src/Data/List/Relation/Binary/Permutation/Setoid/Properties.agda
index e09251caf5..3af753e826 100644
--- a/src/Data/List/Relation/Binary/Permutation/Setoid/Properties.agda
+++ b/src/Data/List/Relation/Binary/Permutation/Setoid/Properties.agda
@@ -200,7 +200,7 @@ shift {v} {w} v≈w (x ∷ xs) ys = begin
 ++-comm []       ys = ↭-sym (++-identityʳ ys)
 ++-comm (x ∷ xs) ys = begin
   x ∷ xs ++ ys   <⟨ ++-comm xs ys ⟩
-  x ∷ ys ++ xs   ↭˘⟨ ↭-shift ys xs ⟩
+  x ∷ ys ++ xs   ↭⟨ ↭-shift ys xs ⟨
   ys ++ (x ∷ xs) ∎
 
 -- Structures
@@ -262,7 +262,7 @@ inject v ws↭ys xs↭zs = trans (++⁺ˡ _ (↭-prep _ xs↭zs)) (++⁺ʳ _ ws
 
 shifts : ∀ xs ys {zs : List A} → xs ++ ys ++ zs ↭ ys ++ xs ++ zs
 shifts xs ys {zs} = begin
-   xs ++ ys  ++ zs ↭˘⟨ ++-assoc xs ys zs ⟩
+   xs ++ ys  ++ zs ↭⟨ ++-assoc xs ys zs ⟨
   (xs ++ ys) ++ zs ↭⟨ ++⁺ʳ zs (++-comm xs ys) ⟩
   (ys ++ xs) ++ zs ↭⟨ ++-assoc ys xs zs ⟩
    ys ++ xs  ++ zs ∎
@@ -297,19 +297,19 @@ dropMiddleElement {v} ws xs {ys} {zs} p = helper p ws xs ≋-refl ≋-refl
   helper {_ ∷ as} {_ ∷ bs} (prep _ as↭bs) [] [] {ys} {zs} (_ ∷ ys≋as) (_ ∷ zs≋bs) = begin
     ys               ≋⟨  ys≋as ⟩
     as               ↭⟨  as↭bs ⟩
-    bs               ≋˘⟨ zs≋bs ⟩
+    bs               ≋⟨ zs≋bs ⟨
     zs               ∎
   helper {_ ∷ as} {_ ∷ bs} (prep a≈b as↭bs) [] (x ∷ xs) {ys} {zs} (≈₁ ∷ ≋₁) (≈₂ ∷ ≋₂) = begin
     ys               ≋⟨  ≋₁ ⟩
     as               ↭⟨  as↭bs ⟩
-    bs               ≋˘⟨ ≋₂ ⟩
+    bs               ≋⟨ ≋₂ ⟨
     xs ++ v ∷ zs     ↭⟨  shift (lemma ≈₁ a≈b ≈₂) xs zs ⟩
     x ∷ xs ++ zs     ∎
   helper {_ ∷ as} {_ ∷ bs} (prep v≈w p) (w ∷ ws) [] {ys} {zs} (≈₁ ∷ ≋₁) (≈₂ ∷ ≋₂) = begin
     w ∷ ws ++ ys     ↭⟨  ↭-sym (shift (lemma ≈₂ (≈-sym v≈w) ≈₁) ws ys) ⟩
     ws ++ v ∷ ys     ≋⟨  ≋₁ ⟩
     as               ↭⟨  p ⟩
-    bs               ≋˘⟨ ≋₂ ⟩
+    bs               ≋⟨ ≋₂ ⟨
     zs               ∎
   helper {_ ∷ as} {_ ∷ bs} (prep w≈x p) (w ∷ ws) (x ∷ xs) {ys} {zs} (≈₁ ∷ ≋₁) (≈₂ ∷ ≋₂) = begin
     w ∷ ws ++ ys     ↭⟨ prep (lemma ≈₁ w≈x ≈₂) (helper p ws xs ≋₁ ≋₂) ⟩
@@ -317,12 +317,12 @@ dropMiddleElement {v} ws xs {ys} {zs} p = helper p ws xs ≋-refl ≋-refl
   helper {_ ∷ a ∷ as} {_ ∷ b ∷ bs} (swap v≈x y≈v p) [] [] {ys} {zs} (≈₁ ∷ ≋₁) (≈₂ ∷ ≋₂) = begin
     ys               ≋⟨  ≋₁ ⟩
     a ∷ as           ↭⟨  prep (≈-trans (≈-trans (≈-trans y≈v (≈-sym ≈₂)) ≈₁) v≈x) p ⟩
-    b ∷ bs           ≋˘⟨ ≋₂ ⟩
+    b ∷ bs           ≋⟨ ≋₂ ⟨
     zs               ∎
   helper {_ ∷ a ∷ as} {_ ∷ b ∷ bs} (swap v≈w y≈w p) [] (x ∷ []) {ys} {zs} (≈₁ ∷ ≋₁) (≈₂ ∷ ≋₂) = begin
     ys               ≋⟨  ≋₁ ⟩
     a ∷ as           ↭⟨  prep y≈w p ⟩
-    _ ∷ bs           ≋˘⟨ ≈₂ ∷ tail ≋₂ ⟩
+    _ ∷ bs           ≋⟨ ≈₂ ∷ tail ≋₂ ⟨
     x ∷ zs           ∎
   helper {_ ∷ a ∷ as} {_ ∷ b ∷ bs} (swap v≈w y≈x p) [] (x ∷ w ∷ xs) {ys} {zs} (≈₁ ∷ ≋₁) (≈₂ ∷ ≋₂) = begin
     ys               ≋⟨ ≋₁ ⟩
@@ -455,8 +455,8 @@ module _ {ℓ} {R : Rel A ℓ} (R? : B.Decidable R) where
   ... | true  | rec | _   = ↭-prep x rec
   ... | false | _   | rec = begin
     y ∷ merge R? (x ∷ xs) ys <⟨ rec ⟩
-    y ∷ x ∷ xs ++ ys         ↭˘⟨ ↭-shift (x ∷ xs) ys ⟩
-    (x ∷ xs) ++ y ∷ ys       ≡˘⟨ Lₚ.++-assoc [ x ] xs (y ∷ ys) ⟩
+    y ∷ x ∷ xs ++ ys         ↭⟨ ↭-shift (x ∷ xs) ys ⟨
+    (x ∷ xs) ++ y ∷ ys       ≡⟨ Lₚ.++-assoc [ x ] xs (y ∷ ys) ⟨
     x ∷ xs ++ y ∷ ys         ∎
     where open PermutationReasoning
 
@@ -497,7 +497,7 @@ module _ {_∙_ : Op₂ A} {ε : A} (isCmonoid : IsCommutativeMonoid _≈_ _∙_
   foldr-commMonoid (prep x≈y xs↭ys) = ∙-cong x≈y (foldr-commMonoid xs↭ys)
   foldr-commMonoid (swap {xs} {ys} {x} {y} {x′} {y′} x≈x′ y≈y′ xs↭ys) = S.begin
     x ∙ (y ∙ foldr _∙_ ε xs)   S.≈⟨ ∙-congˡ (∙-congˡ (foldr-commMonoid xs↭ys)) ⟩
-    x ∙ (y ∙ foldr _∙_ ε ys)   S.≈˘⟨ assoc x y (foldr _∙_ ε ys) ⟩
+    x ∙ (y ∙ foldr _∙_ ε ys)   S.≈⟨ assoc x y (foldr _∙_ ε ys) ⟨
     (x ∙ y) ∙ foldr _∙_ ε ys   S.≈⟨ ∙-congʳ (comm x y) ⟩
     (y ∙ x) ∙ foldr _∙_ ε ys   S.≈⟨ ∙-congʳ (∙-cong y≈y′ x≈x′) ⟩
     (y′ ∙ x′) ∙ foldr _∙_ ε ys S.≈⟨ assoc y′ x′ (foldr _∙_ ε ys) ⟩
diff --git a/src/Data/List/Relation/Binary/Subset/Setoid/Properties.agda b/src/Data/List/Relation/Binary/Subset/Setoid/Properties.agda
index bb20fd417f..0c344758b7 100644
--- a/src/Data/List/Relation/Binary/Subset/Setoid/Properties.agda
+++ b/src/Data/List/Relation/Binary/Subset/Setoid/Properties.agda
@@ -118,7 +118,7 @@ module ⊆-Reasoning (S : Setoid a ℓ) where
   private module Base = PreorderReasoning (⊆-preorder S)
 
   open Base public
-    hiding (step-≲; step-≈; step-≈˘; step-∼)
+    hiding (step-≈; step-≈˘; step-≈-⟩; step-≈-⟨; step-≲; step-∼)
     renaming (≲-go to ⊆-go; ≈-go to ≋-go)
 
   open begin-membership-syntax _IsRelatedTo_ _∈_ (λ x → Base.begin x) public
diff --git a/src/Data/List/Relation/Unary/Any/Properties.agda b/src/Data/List/Relation/Unary/Any/Properties.agda
index b88bdfbe95..e356e9eca1 100644
--- a/src/Data/List/Relation/Unary/Any/Properties.agda
+++ b/src/Data/List/Relation/Unary/Any/Properties.agda
@@ -686,7 +686,7 @@ module _ {A B : Set ℓ} {P : B → Set p} {f : A → List B} where
   Any (λ f → Any (P ∘ f) xs) fs                ↔⟨ Any-cong (λ _ → Any-cong (λ _ → pure↔) (_ ∎)) (_ ∎) ⟩
   Any (λ f → Any (Any P ∘ pure ∘ f) xs) fs     ↔⟨ Any-cong (λ _ → >>=↔ ) (_ ∎) ⟩
   Any (λ f → Any P (xs >>= pure ∘ f)) fs       ↔⟨ >>=↔ ⟩
-  Any P (fs >>= λ f → xs >>= λ x → pure (f x)) ≡˘⟨ P.cong (Any P) (Listₑ.Applicative.unfold-⊛ fs xs) ⟩
+  Any P (fs >>= λ f → xs >>= λ x → pure (f x)) ≡⟨ P.cong (Any P) (Listₑ.Applicative.unfold-⊛ fs xs) ⟨
   Any P (fs ⊛ xs)                               ∎
   where open Related.EquationalReasoning
 
@@ -706,7 +706,7 @@ module _ {A B : Set ℓ} {P : B → Set p} {f : A → List B} where
   Any (λ x → Any (λ y → P (x , y)) ys) xs                           ↔⟨ pure↔ ⟩
   Any (λ _,_ → Any (λ x → Any (λ y → P (x , y)) ys) xs) (pure _,_)  ↔⟨ ⊛↔ ⟩
   Any (λ x, → Any (P ∘ x,) ys) (pure _,_ ⊛ xs)                      ↔⟨ ⊛↔ ⟩
-  Any P (pure _,_ ⊛ xs ⊛ ys)                                        ≡˘⟨ P.cong (Any P ∘′ (_⊛ ys)) (Listₑ.Applicative.unfold-<$> _,_ xs) ⟩
+  Any P (pure _,_ ⊛ xs ⊛ ys)                                        ≡⟨ P.cong (Any P ∘′ (_⊛ ys)) (Listₑ.Applicative.unfold-<$> _,_ xs) ⟨
   Any P (xs ⊗ ys)                                                   ∎
   where open Related.EquationalReasoning
 
diff --git a/src/Data/Nat/Binary/Properties.agda b/src/Data/Nat/Binary/Properties.agda
index 9e8976842e..f83bbfc12c 100644
--- a/src/Data/Nat/Binary/Properties.agda
+++ b/src/Data/Nat/Binary/Properties.agda
@@ -156,9 +156,9 @@ fromℕ≡fromℕ' n = fromℕ-helper≡fromℕ' n n ℕₚ.≤-refl
   tail-homo ℕ.zero = refl
   tail-homo (ℕ.suc ℕ.zero) = refl
   tail-homo (ℕ.suc (ℕ.suc n)) = begin
-    tail (suc (fromℕ' (ℕ.suc (ℕ.suc n))))  ≡˘⟨ tail-suc (fromℕ' n) ⟩
+    tail (suc (fromℕ' (ℕ.suc (ℕ.suc n))))  ≡⟨ tail-suc (fromℕ' n) ⟨
     suc (tail (suc (fromℕ' n)))            ≡⟨ cong suc (tail-homo n) ⟩
-    fromℕ' (ℕ.suc (n / 2))                 ≡˘⟨ cong fromℕ' (+-distrib-/-∣ˡ {2} n ∣-refl) ⟩
+    fromℕ' (ℕ.suc (n / 2))                 ≡⟨ cong fromℕ' (+-distrib-/-∣ˡ {2} n ∣-refl) ⟨
     fromℕ' (ℕ.suc (ℕ.suc n) / 2)           ∎
 
   fromℕ-helper≡fromℕ' : ∀ n w → n ℕ.≤ w → fromℕ.helper n n w ≡ fromℕ' n
@@ -167,7 +167,7 @@ fromℕ≡fromℕ' n = fromℕ-helper≡fromℕ' n n ℕₚ.≤-refl
     split-injective (begin
       split (fromℕ.helper n (ℕ.suc n) (ℕ.suc w))         ≡⟨ split-if _ _ ⟩
       just (n % 2 ℕ.≡ᵇ 0) , fromℕ.helper n (n / 2) w     ≡⟨ cong (_ ,_) rec-n/2 ⟩
-      just (n % 2 ℕ.≡ᵇ 0) , fromℕ' (n / 2)               ≡˘⟨ cong₂ _,_ (head-homo n) (tail-homo n) ⟩
+      just (n % 2 ℕ.≡ᵇ 0) , fromℕ' (n / 2)               ≡⟨ cong₂ _,_ (head-homo n) (tail-homo n) ⟨
       head (fromℕ' (ℕ.suc n)) , tail (fromℕ' (ℕ.suc n))  ≡⟨⟩
       split (fromℕ' (ℕ.suc n))                           ∎)
     where rec-n/2 = fromℕ-helper≡fromℕ' (n / 2) w (ℕₚ.≤-trans (m/n≤m n 2) n≤w)
@@ -613,7 +613,7 @@ module ≤-Reasoning where
     <-≤-trans
     ≤-<-trans
     public
-    hiding (step-≈; step-≈˘)
+    hiding (step-≈; step-≈˘; step-≈-⟩; step-≈-⟨)
 
 ------------------------------------------------------------------------
 -- Properties of _<ℕ_
diff --git a/src/Data/Nat/Combinatorics.agda b/src/Data/Nat/Combinatorics.agda
index fc6ef422b4..d07d22db47 100644
--- a/src/Data/Nat/Combinatorics.agda
+++ b/src/Data/Nat/Combinatorics.agda
@@ -66,9 +66,9 @@ open Specification public
 nCk≡nC[n∸k] : k ≤ n → n C k ≡ n C (n ∸ k)
 nCk≡nC[n∸k] {k} {n} k≤n = begin-equality
   n C k                               ≡⟨ nCk≡n!/k![n-k]! k≤n ⟩
-  n ! / (k ! * (n ∸ k) !)             ≡˘⟨ /-congʳ (*-comm ((n ∸ k) !) (k !)) ⟩
-  n ! / ((n ∸ k) ! * k !)             ≡˘⟨ /-congʳ (cong ((n ∸ k) ! *_) (cong _! (m∸[m∸n]≡n k≤n))) ⟩
-  n ! / ((n ∸ k) ! * (n ∸ (n ∸ k)) !) ≡˘⟨ nCk≡n!/k![n-k]! (m≤n⇒n∸m≤n k≤n) ⟩
+  n ! / (k ! * (n ∸ k) !)             ≡⟨ /-congʳ (*-comm ((n ∸ k) !) (k !)) ⟨
+  n ! / ((n ∸ k) ! * k !)             ≡⟨ /-congʳ (cong ((n ∸ k) ! *_) (cong _! (m∸[m∸n]≡n k≤n))) ⟨
+  n ! / ((n ∸ k) ! * (n ∸ (n ∸ k)) !) ≡⟨ nCk≡n!/k![n-k]! (m≤n⇒n∸m≤n k≤n) ⟨
   n C (n ∸ k)                         ∎
   where instance
     _ = (n ∸ k) !* k !≢0
@@ -78,9 +78,9 @@ nCk≡nC[n∸k] {k} {n} k≤n = begin-equality
 nCk≡nPk/k! : k ≤ n → n C k ≡ ((n P k) / k !) {{k !≢0}}
 nCk≡nPk/k! {k} {n} k≤n = begin-equality
   n C k                   ≡⟨ nCk≡n!/k![n-k]! k≤n ⟩
-  n ! / (k ! * (n ∸ k) !) ≡˘⟨ /-congʳ (*-comm ((n ∸ k)!) (k !)) ⟩
-  n ! / ((n ∸ k) ! * k !) ≡˘⟨ m/n/o≡m/[n*o] (n !) ((n ∸ k) !) (k !) ⟩
-  (n ! / (n ∸ k) !) / k ! ≡˘⟨ /-congˡ (nPk≡n!/[n∸k]! k≤n) ⟩
+  n ! / (k ! * (n ∸ k) !) ≡⟨ /-congʳ (*-comm ((n ∸ k)!) (k !)) ⟨
+  n ! / ((n ∸ k) ! * k !) ≡⟨ m/n/o≡m/[n*o] (n !) ((n ∸ k) !) (k !) ⟨
+  (n ! / (n ∸ k) !) / k ! ≡⟨ /-congˡ (nPk≡n!/[n∸k]! k≤n) ⟨
   (n P k) / k !           ∎
   where instance
     _ = k !≢0
@@ -128,7 +128,7 @@ module _ {n k} (k<n : k < n) where
       [n-k] * [n-k-1]!
         ≡⟨ cong (_* [n-k-1]!) [n-k]≡1+[n-k-1] ⟩
       (suc [n-k-1]) * [n-k-1]!
-        ≡˘⟨ cong _! [n-k]≡1+[n-k-1] ⟩
+        ≡⟨ cong _! [n-k]≡1+[n-k-1] ⟨
       [n-k]!                ∎
 
   private
@@ -163,39 +163,39 @@ nCk+nC[k+1]≡[n+1]C[k+1] n k with <-cmp k n
   n C k + n C (suc k) ≡⟨ cong (_+ (n C (suc k))) (k>n⇒nCk≡0 k>n) ⟩
   0 + n C (suc k)     ≡⟨⟩
   n C (suc k)         ≡⟨ k>n⇒nCk≡0 (m<n⇒m<1+n k>n) ⟩
-  0                   ≡˘⟨ k>n⇒nCk≡0 (s<s k>n) ⟩
+  0                   ≡⟨ k>n⇒nCk≡0 (s<s k>n) ⟨
   suc n C suc k       ∎
 {- case k≡n, in which case 1+k≡1+n>n -}
 ... | tri≈ _ k≡n _ rewrite k≡n = begin-equality
   n C n + n C (suc n) ≡⟨ cong (n C n +_) (k>n⇒nCk≡0 (n<1+n n)) ⟩
   n C n + 0           ≡⟨ +-identityʳ (n C n) ⟩
   n C n               ≡⟨ nCn≡1 n ⟩
-  1                   ≡˘⟨ nCn≡1 (suc n) ⟩
+  1                   ≡⟨ nCn≡1 (suc n) ⟨
   suc n C suc n       ∎
 {- case k<n, in which case 1+k<1+n and there's arithmetic to perform -}
 ... | tri< k<n _ _ = begin-equality
   n C k + n C (suc k)
     ≡⟨ cong (n C k +_) (nCk≡n!/k![n-k]! k<n)  ⟩
   n C k + (n! / d[k+1])
-    ≡˘⟨ cong (n C k +_) (m*n/m*o≡n/o (n ∸ k) n! d[k+1]) ⟩
+    ≡⟨ cong (n C k +_) (m*n/m*o≡n/o (n ∸ k) n! d[k+1]) ⟨
   n C k + [n-k]*n!/[n-k]*d[k+1]
     ≡⟨ cong (_+ [n-k]*n!/[n-k]*d[k+1]) (nCk≡n!/k![n-k]! k≤n) ⟩
   n! / d[k] + _
-    ≡˘⟨ cong (_+ [n-k]*n!/[n-k]*d[k+1]) (m*n/m*o≡n/o (suc k) n! d[k]) ⟩
+    ≡⟨ cong (_+ [n-k]*n!/[n-k]*d[k+1]) (m*n/m*o≡n/o (suc k) n! d[k]) ⟨
   (suc k * n!) / [k+1]*d[k] + _
     ≡⟨ cong (((suc k * n!) / [k+1]*d[k]) +_) (/-congʳ ([n-k]*d[k+1]≡[k+1]*d[k] k<n)) ⟩
   (suc k * n!) / [k+1]*d[k] + ((n ∸ k) * n! / [k+1]*d[k])
-    ≡˘⟨ +-distrib-/-∣ˡ _ (*-monoʳ-∣ (suc k) (k![n∸k]!∣n! k≤n)) ⟩
+    ≡⟨ +-distrib-/-∣ˡ _ (*-monoʳ-∣ (suc k) (k![n∸k]!∣n! k≤n)) ⟨
   ((suc k) * n! + (n ∸ k) * n!) / [k+1]*d[k]
-    ≡˘⟨ cong (_/ [k+1]*d[k]) (*-distribʳ-+ (n !) (suc k) (n ∸ k)) ⟩
+    ≡⟨ cong (_/ [k+1]*d[k]) (*-distribʳ-+ (n !) (suc k) (n ∸ k)) ⟨
   ((suc k + (n ∸ k)) * n !) / [k+1]*d[k]
     ≡⟨ cong (λ z → z * n ! / [k+1]*d[k]) [k+1]+[n-k]≡[n+1] ⟩
   ((suc n) * n !) / [k+1]*d[k]
-    ≡˘⟨ /-congʳ (*-assoc (suc k) (k !) ((n ∸ k) !)) ⟩
+    ≡⟨ /-congʳ (*-assoc (suc k) (k !) ((n ∸ k) !)) ⟨
   ((suc n) * n !) / (((suc k) * k !) * (n ∸ k) !)
     ≡⟨⟩
   suc n ! / (suc k ! * (suc n ∸ suc k) !)
-    ≡˘⟨ nCk≡n!/k![n-k]! [k+1]≤[n+1] ⟩
+    ≡⟨ nCk≡n!/k![n-k]! [k+1]≤[n+1] ⟨
   suc n C suc k ∎
   where
     k≤n                     : k ≤ n
diff --git a/src/Data/Nat/Combinatorics/Specification.agda b/src/Data/Nat/Combinatorics/Specification.agda
index 522e3104ed..b217ea4143 100644
--- a/src/Data/Nat/Combinatorics/Specification.agda
+++ b/src/Data/Nat/Combinatorics/Specification.agda
@@ -40,7 +40,7 @@ nP′k≡n!/[n∸k]! : ∀ {n k} → k ≤ n → n P′ k ≡ (n ! / (n ∸ k) !
 nP′k≡n!/[n∸k]! {n} {zero}  z≤n = sym (n/n≡1 (n !) {{n !≢0}})
 nP′k≡n!/[n∸k]! {n} {suc k} k<n = begin-equality
   (n ∸ k) * (n P′ k)             ≡⟨ cong ((n ∸ k) *_) (nP′k≡n!/[n∸k]! (<⇒≤ k<n)) ⟩
-  (n ∸ k) * (n ! / (n ∸ k) !)    ≡˘⟨ *-/-assoc (n ∸ k) (m≤n⇒m!∣n! (m∸n≤m n k)) ⟩
+  (n ∸ k) * (n ! / (n ∸ k) !)    ≡⟨ *-/-assoc (n ∸ k) (m≤n⇒m!∣n! (m∸n≤m n k)) ⟨
   (((n ∸ k) * n !) / (n ∸ k) !)  ≡⟨ m*n/m!≡n/[m∸1]! (n ∸ k) (n !) ⟩
   (n ! / (pred (n ∸ k) !))       ≡⟨ /-congʳ (cong _! (pred[m∸n]≡m∸[1+n] n k)) ⟩
   (n ! / (n ∸ suc k) !)          ∎
@@ -67,7 +67,7 @@ P′-rec : ∀ {n k} → k ≤ n → .{{NonZero k}} →
         n P′ k ≡ k * (pred n P′ pred k) + pred n P′ k
 P′-rec n@{suc n-1} k@{suc k-1} k≤n = begin-equality
   n P′ k                                        ≡⟨ nP′k≡n[n∸1P′k∸1] n k ⟩
-  n * (n-1 P′ k-1)                              ≡˘⟨ cong (_* (n-1 P′ k-1)) (m+[n∸m]≡n {k} {n} k≤n) ⟩
+  n * (n-1 P′ k-1)                              ≡⟨ cong (_* (n-1 P′ k-1)) (m+[n∸m]≡n {k} {n} k≤n) ⟨
   (k + (n ∸ k)) * (n-1 P′ k-1)                  ≡⟨ *-distribʳ-+ (n-1 P′ k-1) k (n ∸ k) ⟩
   k * (n-1 P′ k-1) + (n-1 ∸ k-1) * (n-1 P′ k-1) ≡⟨⟩
   k * (n-1 P′ k-1) + (n-1 P′ k)                 ∎
@@ -89,7 +89,7 @@ k!∣nP′k n@{suc n-1} k@{suc k-1} k≤n@(s≤s k-1≤n-1) with k-1 ≟ n-1
 ... | no  k≢n  = begin
   k !                           ≡⟨⟩
   k * k-1 !                     ∣⟨ ∣m∣n⇒∣m+n (*-monoʳ-∣ k (k!∣nP′k k-1≤n-1)) ( k!∣nP′k (≤∧≢⇒< k-1≤n-1 k≢n)) ⟩
-  k * (n-1 P′ k-1) + (n-1 P′ k) ≡˘⟨ P′-rec k≤n ⟩
+  k * (n-1 P′ k-1) + (n-1 P′ k) ≡⟨ P′-rec k≤n ⟨
   n P′ k                        ∎
   where open ∣-Reasoning
 
@@ -134,7 +134,7 @@ C′-sym {n} {k} k≤n = begin-equality
   n C′ (n ∸ k)                        ≡⟨ nC′k≡n!/k![n-k]! {n} {n ∸ k} (m≤n⇒n∸m≤n k≤n) ⟩
   n ! / ((n ∸ k) ! * (n ∸ (n ∸ k)) !) ≡⟨ /-congʳ (cong ((n ∸ k) ! *_) (cong _! (m∸[m∸n]≡n k≤n))) ⟩
   n ! / ((n ∸ k) ! * k !)             ≡⟨ /-congʳ (*-comm ((n ∸ k) !) (k !)) ⟩
-  n ! / (k ! * (n ∸ k) !)             ≡˘⟨ nC′k≡n!/k![n-k]! k≤n ⟩
+  n ! / (k ! * (n ∸ k) !)             ≡⟨ nC′k≡n!/k![n-k]! k≤n ⟨
   n C′ k                              ∎
   where
   open ≤-Reasoning
diff --git a/src/Data/Nat/DivMod.agda b/src/Data/Nat/DivMod.agda
index dbe99a30e6..bbb8288838 100644
--- a/src/Data/Nat/DivMod.agda
+++ b/src/Data/Nat/DivMod.agda
@@ -41,8 +41,8 @@ m≡m%n+[m/n]*n m (suc n) = div-mod-lemma 0 0 m n
 
 m%n≡m∸m/n*n : ∀ m n .{{_ : NonZero n}} → m % n ≡ m ∸ (m / n) * n
 m%n≡m∸m/n*n m n = begin-equality
-  m % n                  ≡˘⟨ m+n∸n≡m (m % n) m/n*n ⟩
-  m % n + m/n*n ∸ m/n*n  ≡˘⟨ cong (_∸ m/n*n) (m≡m%n+[m/n]*n m n) ⟩
+  m % n                  ≡⟨ m+n∸n≡m (m % n) m/n*n ⟨
+  m % n + m/n*n ∸ m/n*n  ≡⟨ cong (_∸ m/n*n) (m≡m%n+[m/n]*n m n) ⟨
   m ∸ m/n*n              ∎
   where m/n*n = (m / n) * n
 
@@ -79,14 +79,14 @@ m%n%n≡m%n m (suc n-1) = modₕ-idem 0 m n-1
 m≤n⇒[n∸m]%m≡n%m : .⦃ _ : NonZero m ⦄ → m ≤ n →
                   (n ∸ m) % m ≡ n % m
 m≤n⇒[n∸m]%m≡n%m {m} {n} m≤n = begin-equality
-  (n ∸ m) % m     ≡˘⟨ [m+n]%n≡m%n (n ∸ m) m ⟩
+  (n ∸ m) % m     ≡⟨ [m+n]%n≡m%n (n ∸ m) m ⟨
   (n ∸ m + m) % m ≡⟨ cong (_% m) (m∸n+n≡m m≤n) ⟩
   n % m           ∎
 
 m*n≤o⇒[o∸m*n]%n≡o%n : ∀ m {n o} .⦃ _ : NonZero n ⦄ → m * n ≤ o →
                       (o ∸ m * n) % n ≡ o % n
 m*n≤o⇒[o∸m*n]%n≡o%n m {n} {o} m*n≤o = begin-equality
-  (o ∸ m * n) % n         ≡˘⟨ [m+kn]%n≡m%n (o ∸ m * n) m n ⟩
+  (o ∸ m * n) % n         ≡⟨ [m+kn]%n≡m%n (o ∸ m * n) m n ⟨
   (o ∸ m * n + m * n) % n ≡⟨ cong (_% n) (m∸n+n≡m m*n≤o) ⟩
   o % n                   ∎
 
@@ -95,7 +95,7 @@ m∣n⇒o%n%m≡o%m : ∀ m n o .⦃ _ : NonZero m ⦄ .⦃ _ : NonZero n ⦄ 
 m∣n⇒o%n%m≡o%m m n@.(p * m) o (divides-refl p) = begin-equality
   o % n % m                ≡⟨⟩
   o % pm % m               ≡⟨ %-congˡ (m%n≡m∸m/n*n o pm) ⟩
-  (o ∸ o / pm * pm) % m    ≡˘⟨ cong (λ # → (o ∸ #) % m) (*-assoc (o / pm) p m) ⟩
+  (o ∸ o / pm * pm) % m    ≡⟨ cong (λ # → (o ∸ #) % m) (*-assoc (o / pm) p m) ⟨
   (o ∸ o / pm * p * m) % m ≡⟨ m*n≤o⇒[o∸m*n]%n≡o%n (o / pm * p) lem ⟩
   o % m                    ∎
   where
@@ -107,7 +107,7 @@ m∣n⇒o%n%m≡o%m m n@.(p * m) o (divides-refl p) = begin-equality
     -- Sort out dependencies in this file, then use m/n*n≤m instead.
     o / pm * pm          ≤⟨ m≤m+n (o / pm * pm) (o % pm) ⟩
     o / pm * pm + o % pm ≡⟨ +-comm _ (o % pm) ⟩
-    o % pm + o / pm * pm ≡˘⟨ m≡m%n+[m/n]*n o pm ⟩
+    o % pm + o / pm * pm ≡⟨ m≡m%n+[m/n]*n o pm ⟨
     o                    ∎
 
 m*n%n≡0 : ∀ m n .{{_ : NonZero n}} → (m * n) % n ≡ 0
@@ -168,8 +168,8 @@ m<[1+n%d]⇒m≤[n%d] {m} n (suc d-1) = k<1+a[modₕ]n⇒k≤a[modₕ]n 0 m n d-
     (m′ + k * d) * (n′ + j * d)                       ≡⟨ *-distribʳ-+ (n′ + j * d) m′ (k * d) ⟩
     m′ * (n′ + j * d) + (k * d) * (n′ + j * d)        ≡⟨ cong₂ _+_ (*-distribˡ-+ m′ n′ (j * d)) (*-comm (k * d) (n′ + j * d)) ⟩
     (m′ * n′ + m′ * (j * d)) + (n′ + j * d) * (k * d) ≡⟨ +-assoc (m′ * n′) (m′ * (j * d)) ((n′ + j * d) * (k * d)) ⟩
-    m′ * n′ + (m′ * (j * d) + (n′ + j * d) * (k * d)) ≡˘⟨ cong (m′ * n′ +_) (cong₂ _+_ (*-assoc m′ j d) (*-assoc (n′ + j * d) k d)) ⟩
-    m′ * n′ + ((m′ * j) * d + ((n′ + j * d) * k) * d) ≡˘⟨ cong (m′ * n′ +_) (*-distribʳ-+ d (m′ * j) ((n′ + j * d) * k)) ⟩
+    m′ * n′ + (m′ * (j * d) + (n′ + j * d) * (k * d)) ≡⟨ cong (m′ * n′ +_) (cong₂ _+_ (*-assoc m′ j d) (*-assoc (n′ + j * d) k d)) ⟨
+    m′ * n′ + ((m′ * j) * d + ((n′ + j * d) * k) * d) ≡⟨ cong (m′ * n′ +_) (*-distribʳ-+ d (m′ * j) ((n′ + j * d) * k)) ⟨
     m′ * n′ + (m′ * j + (n′ + j * d) * k) * d         ∎
 
 %-remove-+ˡ : ∀ {m} n {d} .{{_ : NonZero d}} → d ∣ m → (m + n) % d ≡ n % d
@@ -242,7 +242,7 @@ m/n<m m n n≥2 = *-cancelʳ-< _ (m / n) m (begin-strict
 /-cancelʳ-≡ : ∀ {m n o} .{{_ : NonZero o}} →
               o ∣ m → o ∣ n → m / o ≡ n / o → m ≡ n
 /-cancelʳ-≡ {m} {n} {o} o∣m o∣n m/o≡n/o = begin-equality
-  m           ≡˘⟨ m*[n/m]≡n {o} {m} o∣m ⟩
+  m           ≡⟨ m*[n/m]≡n {o} {m} o∣m ⟨
   o * (m / o) ≡⟨  cong (o *_) m/o≡n/o ⟩
   o * (n / o) ≡⟨  m*[n/m]≡n {o} {n} o∣n ⟩
   n           ∎
@@ -294,10 +294,10 @@ m*n/m*o≡n/o m@(suc _) n o = helper (<-wellFounded n)
   ... | yes n<o = trans (m<n⇒m/n≡0 (*-monoʳ-< m n<o)) (sym (m<n⇒m/n≡0 n<o))
   ... | no  n≮o = begin-equality
     (m * n) / (m * o)             ≡⟨  m/n≡1+[m∸n]/n (*-monoʳ-≤ m (≮⇒≥ n≮o)) ⟩
-    1 + (m * n ∸ m * o) / (m * o) ≡˘⟨ cong (λ v → 1 + v / (m * o)) (*-distribˡ-∸ m n o) ⟩
+    1 + (m * n ∸ m * o) / (m * o) ≡⟨ cong (λ v → 1 + v / (m * o)) (*-distribˡ-∸ m n o) ⟨
     1 + (m * (n ∸ o)) / (m * o)   ≡⟨  cong suc (helper (rec n∸o<n)) ⟩
-    1 + (n ∸ o) / o               ≡˘⟨ cong₂ _+_ (n/n≡1 o) refl ⟩
-    o / o + (n ∸ o) / o           ≡˘⟨ +-distrib-/-∣ˡ (n ∸ o) (divides 1 ((sym (*-identityˡ o)))) ⟩
+    1 + (n ∸ o) / o               ≡⟨ cong₂ _+_ (n/n≡1 o) refl ⟨
+    o / o + (n ∸ o) / o           ≡⟨ +-distrib-/-∣ˡ (n ∸ o) (divides 1 ((sym (*-identityˡ o)))) ⟨
     (o + (n ∸ o)) / o             ≡⟨  cong (_/ o) (m+[n∸m]≡n (≮⇒≥ n≮o)) ⟩
     n / o                         ∎
     where n∸o<n = ∸-monoʳ-< (n≢0⇒n>0 (≢-nonZero⁻¹ o)) (≮⇒≥ n≮o)
@@ -333,19 +333,19 @@ m<n*o⇒m/o<n {m} {suc n} {o} m<n*o with m <? o
 ... | yes m<n = begin-equality
   (m ∸ n) / n  ≡⟨ m<n⇒m/n≡0 (≤-<-trans (m∸n≤m m n) m<n) ⟩
   0            ≡⟨⟩
-  0 ∸ 1        ≡˘⟨ cong (_∸ 1) (m<n⇒m/n≡0 m<n) ⟩
+  0 ∸ 1        ≡⟨ cong (_∸ 1) (m<n⇒m/n≡0 m<n) ⟨
   m / n ∸ 1    ≡⟨⟩
   pred (m / n) ∎
 ... | no m≮n = begin-equality
   (m ∸ n) / n           ≡⟨⟩
-  suc ((m ∸ n) / n) ∸ 1 ≡˘⟨ cong (_∸ 1) (m/n≡1+[m∸n]/n (≮⇒≥ m≮n)) ⟩
+  suc ((m ∸ n) / n) ∸ 1 ≡⟨ cong (_∸ 1) (m/n≡1+[m∸n]/n (≮⇒≥ m≮n)) ⟨
   m / n ∸ 1             ≡⟨⟩
   pred (m / n)          ∎
 
 [m∸n*o]/o≡m/o∸n : ∀ m n o .⦃ _ : NonZero o ⦄ → (m ∸ n * o) / o ≡ m / o ∸ n
 [m∸n*o]/o≡m/o∸n m zero    o = refl
 [m∸n*o]/o≡m/o∸n m (suc n) o = begin-equality
-  (m ∸ (o + n * o)) / o ≡˘⟨ /-congˡ (∸-+-assoc m o (n * o)) ⟩
+  (m ∸ (o + n * o)) / o ≡⟨ /-congˡ (∸-+-assoc m o (n * o)) ⟨
   (m ∸ o ∸ n * o) / o   ≡⟨ [m∸n*o]/o≡m/o∸n (m ∸ o) n o ⟩
   (m ∸ o) / o ∸ n       ≡⟨ cong (_∸ n) ([m∸n]/n≡m/n∸1 m o) ⟩
   m / o ∸ 1 ∸ n         ≡⟨ ∸-+-assoc (m / o) 1 n ⟩
@@ -368,13 +368,13 @@ m/n/o≡m/[n*o] m n o = begin-equality
   lem₁ : n ∣ m / n*o * n*o
   lem₁ = divides (m / n*o * o) $ begin-equality
     m / n*o * n*o   ≡⟨ cong (m / n*o *_) (*-comm n o) ⟩
-    m / n*o * o*n   ≡˘⟨ *-assoc (m / n*o) o n ⟩
+    m / n*o * o*n   ≡⟨ *-assoc (m / n*o) o n ⟨
     m / n*o * o * n ∎
 
   lem₂ : m / n*o * n*o / n ≡ m / n*o * o
   lem₂ = begin-equality
     m / n*o * n*o / n   ≡⟨ cong (λ # → m / n*o * # / n) (*-comm n o) ⟩
-    m / n*o * o*n / n   ≡˘⟨ /-congˡ (*-assoc (m / n*o) o n) ⟩
+    m / n*o * o*n / n   ≡⟨ /-congˡ (*-assoc (m / n*o) o n) ⟨
     m / n*o * o * n / n ≡⟨ m*n/n≡m (m / n*o * o) n ⟩
     m / n*o * o         ∎
 
@@ -395,7 +395,7 @@ m/n/o≡m/[n*o] m n o = begin-equality
                   o ∣ m → p ∣ n → (m * n) / (o * p) ≡ (m / o) * (n / p)
 /-*-interchange {m} {n} {o@(suc _)} {p@(suc _)} o∣m p∣n = *-cancelˡ-≡ _ _ (o * p) (begin-equality
   (o * p) * ((m * n) / (o * p)) ≡⟨  m*[n/m]≡n (*-pres-∣ o∣m p∣n) ⟩
-  m * n                         ≡˘⟨ cong₂ _*_ (m*[n/m]≡n o∣m) (m*[n/m]≡n p∣n) ⟩
+  m * n                         ≡⟨ cong₂ _*_ (m*[n/m]≡n o∣m) (m*[n/m]≡n p∣n) ⟨
   (o * (m / o)) * (p * (n / p)) ≡⟨ [m*n]*[o*p]≡[m*o]*[n*p] o (m / o) p (n / p) ⟩
   (o * p) * ((m / o) * (n / p)) ∎)
 
@@ -407,11 +407,11 @@ m%[n*o]/o≡m/o%n : ∀ m n o .⦃ _ : NonZero n ⦄ .⦃ _ : NonZero o ⦄
                   ⦃ _ : NonZero (n * o) ⦄ → m % (n * o) / o ≡ m / o % n
 m%[n*o]/o≡m/o%n m n o ⦃ _ ⦄ ⦃ _ ⦄ ⦃ n*o≢0 ⦄ = begin-equality
   m % (n * o) / o                   ≡⟨ /-congˡ (m%n≡m∸m/n*n m (n * o)) ⟩
-  (m ∸ (m / (n * o) * (n * o))) / o ≡˘⟨ cong (λ # → (m ∸ #) / o) (*-assoc (m / (n * o)) n o) ⟩
+  (m ∸ (m / (n * o) * (n * o))) / o ≡⟨ cong (λ # → (m ∸ #) / o) (*-assoc (m / (n * o)) n o) ⟨
   (m ∸ (m / (n * o) * n * o)) / o   ≡⟨ [m∸n*o]/o≡m/o∸n m (m / (n * o) * n) o ⟩
   m / o ∸ m / (n * o) * n           ≡⟨ cong (λ # → m / o ∸ # * n) (/-congʳ (*-comm n o)) ⟩
-  m / o ∸ m / (o * n) * n           ≡˘⟨ cong (λ # → m / o ∸ # * n) (m/n/o≡m/[n*o] m o n ) ⟩
-  m / o ∸ m / o / n * n             ≡˘⟨ m%n≡m∸m/n*n (m / o) n ⟩
+  m / o ∸ m / (o * n) * n           ≡⟨ cong (λ # → m / o ∸ # * n) (m/n/o≡m/[n*o] m o n ) ⟨
+  m / o ∸ m / o / n * n             ≡⟨ m%n≡m∸m/n*n (m / o) n ⟨
   m / o % n                         ∎
   where instance o*n≢0 = subst NonZero (*-comm n o) n*o≢0
 
@@ -420,9 +420,9 @@ m%n*o≡m*o%[n*o] : ∀ m n o .⦃ _ : NonZero n ⦄ ⦃ _ : NonZero (n * o) ⦄
 m%n*o≡m*o%[n*o] m n o ⦃ _ ⦄ ⦃ n*o≢0 ⦄ = begin-equality
   m % n * o                         ≡⟨ cong (_* o) (m%n≡m∸m/n*n m n) ⟩
   (m ∸ m / n * n) * o               ≡⟨ *-distribʳ-∸ o m (m / n * n) ⟩
-  m * o ∸ m / n * n * o             ≡˘⟨ cong (λ # → m * o ∸ # * n * o) (m*n/o*n≡m/o m o n) ⟩
+  m * o ∸ m / n * n * o             ≡⟨ cong (λ # → m * o ∸ # * n * o) (m*n/o*n≡m/o m o n) ⟨
   m * o ∸ m * o / (n * o) * n * o   ≡⟨ cong (m * o ∸_) (*-assoc (m * o / (n * o)) n o) ⟩
-  m * o ∸ m * o / (n * o) * (n * o) ≡˘⟨ m%n≡m∸m/n*n (m * o) (n * o) ⟩
+  m * o ∸ m * o / (n * o) * (n * o) ≡⟨ m%n≡m∸m/n*n (m * o) (n * o) ⟨
   m * o % (n * o)                   ∎
 
 [m*n+o]%[p*n]≡[m*n]%[p*n]+o : ∀ m {n o} p ⦃ _ : NonZero (p * n) ⦄ → o < n →
@@ -438,7 +438,7 @@ m%n*o≡m*o%[n*o] m n o ⦃ _ ⦄ ⦃ n*o≢0 ⦄ = begin-equality
 
   lem₁ : mn % pn ≤ p-1 * n
   lem₁ = begin
-    mn % pn     ≡˘⟨ m%n*o≡m*o%[n*o] m p n ⟩
+    mn % pn     ≡⟨ m%n*o≡m*o%[n*o] m p n ⟨
     (m % p) * n ≤⟨ *-monoˡ-≤ n (m<1+n⇒m≤n (m%n<n m p)) ⟩
     p-1 * n     ∎
 
@@ -470,7 +470,7 @@ _divMod_ : (dividend divisor : ℕ) .{{_ : NonZero divisor}} →
            DivMod dividend divisor
 m divMod n = result (m / n) (m mod n) $ begin-equality
   m                               ≡⟨  m≡m%n+[m/n]*n m n ⟩
-  m % n                + [m/n]*n  ≡˘⟨ cong (_+ [m/n]*n) (toℕ-fromℕ< [m%n]<n) ⟩
+  m % n                + [m/n]*n  ≡⟨ cong (_+ [m/n]*n) (toℕ-fromℕ< [m%n]<n) ⟨
   toℕ (fromℕ< [m%n]<n) + [m/n]*n  ∎
   where [m/n]*n = m / n * n ; [m%n]<n = m%n<n m n
 
diff --git a/src/Data/Nat/DivMod/WithK.agda b/src/Data/Nat/DivMod/WithK.agda
index 3f6047df60..10ef4c4f21 100644
--- a/src/Data/Nat/DivMod/WithK.agda
+++ b/src/Data/Nat/DivMod/WithK.agda
@@ -36,6 +36,6 @@ _divMod_ : (dividend divisor : ℕ) → .{{ NonZero divisor }} →
            DivMod dividend divisor
 m divMod n = result (m / n) (m mod n) $ ≡-erase $ begin
   m                                 ≡⟨ m≡m%n+[m/n]*n m n ⟩
-  m % n                  + [m/n]*n  ≡˘⟨ cong (_+ [m/n]*n) (toℕ-fromℕ<″ lemma″) ⟩
+  m % n                  + [m/n]*n  ≡⟨ cong (_+ [m/n]*n) (toℕ-fromℕ<″ lemma″) ⟨
   toℕ (fromℕ<″ _ lemma″) + [m/n]*n  ∎
   where [m/n]*n = m / n * n ; lemma″ = ≤″-erase (≤⇒≤″ (m%n<n m n))
diff --git a/src/Data/Nat/Divisibility.agda b/src/Data/Nat/Divisibility.agda
index 63037a49b2..bb30716e01 100644
--- a/src/Data/Nat/Divisibility.agda
+++ b/src/Data/Nat/Divisibility.agda
@@ -121,7 +121,7 @@ module ∣-Reasoning where
   private module Base = PreorderReasoning ∣-preorder
 
   open Base public
-    hiding (step-≈; step-≈˘; step-∼; step-≲)
+    hiding (step-≈; step-≈˘; step-≈-⟩; step-≈-⟨; step-∼; step-≲)
     renaming (≲-go to ∣-go)
 
   open ∣-syntax _IsRelatedTo_ _IsRelatedTo_ ∣-go public
@@ -293,9 +293,9 @@ m∣n*o⇒m/n∣o {m@.(p * n)} {n@(suc _)} {o} (divides-refl p) pn∣on = begin
   divides (a ∸ m / n * b) $ begin-equality
     m % n                   ≡⟨  m%n≡m∸m/n*n m n ⟩
     m ∸ m / n * n           ≡⟨  cong (λ v → m ∸ m / n * v) 1+n≡bd ⟩
-    m ∸ m / n * (b * d)     ≡˘⟨ cong (m ∸_) (*-assoc (m / n) b d) ⟩
+    m ∸ m / n * (b * d)     ≡⟨ cong (m ∸_) (*-assoc (m / n) b d) ⟨
     m  ∸ (m / n * b) * d    ≡⟨⟩
-    a * d ∸ (m / n * b) * d ≡˘⟨ *-distribʳ-∸ d a (m / n * b) ⟩
+    a * d ∸ (m / n * b) * d ≡⟨ *-distribʳ-∸ d a (m / n * b) ⟨
     (a ∸ m / n * b) * d     ∎
   where open ≤-Reasoning
 
diff --git a/src/Data/Nat/LCM.agda b/src/Data/Nat/LCM.agda
index 5dff2eb530..aead0fbf01 100644
--- a/src/Data/Nat/LCM.agda
+++ b/src/Data/Nat/LCM.agda
@@ -53,9 +53,9 @@ n∣lcm[m,n] : ∀ m n → n ∣ lcm m n
 n∣lcm[m,n] zero        n = n ∣0
 n∣lcm[m,n] m@(suc m-1) n = begin
   n                 ∣⟨  m∣m*n (m / gcd m n) ⟩
-  n * (m / gcd m n) ≡˘⟨ *-/-assoc n (gcd[m,n]∣m m n) ⟩
+  n * (m / gcd m n) ≡⟨ *-/-assoc n (gcd[m,n]∣m m n) ⟨
   n * m / gcd m n   ≡⟨  cong (_/ gcd m n) (*-comm n m) ⟩
-  m * n / gcd m n   ≡˘⟨ rearrange m n ⟩
+  m * n / gcd m n   ≡⟨ rearrange m n ⟨
   m * (n / gcd m n) ∎
   where open ∣-Reasoning; instance _ = gcd≢0ˡ {m} {n}
 
@@ -74,7 +74,7 @@ lcm-least {m@(suc _)} {n} {c} m∣c n∣c = P.subst (_∣ c) (sym (rearrange m n
   mn∣c*gcd : m * n ∣ c * gcd m n
   mn∣c*gcd = begin
     m * n               ∣⟨  gcd-greatest (P.subst (_∣ c * m) (*-comm n m) (*-monoˡ-∣ m n∣c)) (*-monoˡ-∣ n m∣c) ⟩
-    gcd (c * m) (c * n) ≡˘⟨ c*gcd[m,n]≡gcd[cm,cn] c m n ⟩
+    gcd (c * m) (c * n) ≡⟨ c*gcd[m,n]≡gcd[cm,cn] c m n ⟨
     c * gcd m n         ∎
 
 ------------------------------------------------------------------------
diff --git a/src/Data/Nat/Primality.agda b/src/Data/Nat/Primality.agda
index 8e72b32be0..361df42b73 100644
--- a/src/Data/Nat/Primality.agda
+++ b/src/Data/Nat/Primality.agda
@@ -99,7 +99,7 @@ euclidsLemma m n {p@(suc (suc _))} p-prime p∣m*n = result
   p∣rmn r = begin
     p           ∣⟨ p∣m*n ⟩
     m * n       ∣⟨ n∣m*n r ⟩
-    r * (m * n) ≡˘⟨ *-assoc r m n ⟩
+    r * (m * n) ≡⟨ *-assoc r m n ⟨
     r * m * n   ∎
 
   result : p ∣ m ⊎ p ∣ n
@@ -114,14 +114,14 @@ euclidsLemma m n {p@(suc (suc _))} p-prime p∣m*n = result
   ... | Bézout.result 1 _ (Bézout.+- r s 1+sp≡rm) =
     inj₂ (flip ∣m+n∣m⇒∣n (n∣m*n*o s n) (begin
       p             ∣⟨ p∣rmn r ⟩
-      r * m * n     ≡˘⟨ cong (_* n) 1+sp≡rm ⟩
+      r * m * n     ≡⟨ cong (_* n) 1+sp≡rm ⟨
       n + s * p * n ≡⟨ +-comm n (s * p * n) ⟩
       s * p * n + n ∎))
 
   ... | Bézout.result 1 _ (Bézout.-+ r s 1+rm≡sp) =
     inj₂ (flip ∣m+n∣m⇒∣n (p∣rmn r) (begin
       p             ∣⟨ n∣m*n*o s n ⟩
-      s * p * n     ≡˘⟨ cong (_* n) 1+rm≡sp ⟩
+      s * p * n     ≡⟨ cong (_* n) 1+rm≡sp ⟨
       n + r * m * n ≡⟨ +-comm n (r * m * n) ⟩
       r * m * n + n ∎))
 
diff --git a/src/Data/Nat/Properties.agda b/src/Data/Nat/Properties.agda
index 74350e1f6b..e304ed659f 100644
--- a/src/Data/Nat/Properties.agda
+++ b/src/Data/Nat/Properties.agda
@@ -498,7 +498,7 @@ module ≤-Reasoning where
     <-≤-trans
     ≤-<-trans
     public
-    hiding (step-≈; step-≈˘)
+    hiding (step-≈; step-≈˘; step-≈-⟩; step-≈-⟨)
 
 open ≤-Reasoning
 
@@ -918,7 +918,7 @@ m*n≡1⇒n≡1 m n eq = m*n≡1⇒m≡1 n m (trans (*-comm n m) eq)
 [m*n]*[o*p]≡[m*o]*[n*p] m n o p = begin-equality
   (m * n) * (o * p) ≡⟨  *-assoc m n (o * p) ⟩
   m * (n * (o * p)) ≡⟨  cong (m *_) (x∙yz≈y∙xz n o p) ⟩
-  m * (o * (n * p)) ≡˘⟨ *-assoc m o (n * p) ⟩
+  m * (o * (n * p)) ≡⟨ *-assoc m o (n * p) ⟨
   (m * o) * (n * p) ∎
   where open CommSemigroupProperties *-commutativeSemigroup
 
@@ -1325,15 +1325,15 @@ m⊔n≤m+n m n with ⊔-sel m n
 *-distribˡ-⊔ m zero o = sym (cong (_⊔ m * o) (*-zeroʳ m))
 *-distribˡ-⊔ m (suc n) zero = begin-equality
   m * (suc n ⊔ zero)         ≡⟨⟩
-  m * suc n                  ≡˘⟨ ⊔-identityʳ (m * suc n) ⟩
-  m * suc n ⊔ zero           ≡˘⟨ cong (m * suc n ⊔_) (*-zeroʳ m) ⟩
+  m * suc n                  ≡⟨ ⊔-identityʳ (m * suc n) ⟨
+  m * suc n ⊔ zero           ≡⟨ cong (m * suc n ⊔_) (*-zeroʳ m) ⟨
   m * suc n ⊔ m * zero       ∎
 *-distribˡ-⊔ m (suc n) (suc o) = begin-equality
   m * (suc n ⊔ suc o)        ≡⟨⟩
   m * suc (n ⊔ o)            ≡⟨ *-suc m (n ⊔ o) ⟩
   m + m * (n ⊔ o)            ≡⟨ cong (m +_) (*-distribˡ-⊔ m n o) ⟩
   m + (m * n ⊔ m * o)        ≡⟨ +-distribˡ-⊔ m (m * n) (m * o) ⟩
-  (m + m * n) ⊔ (m + m * o)  ≡˘⟨ cong₂ _⊔_ (*-suc m n) (*-suc m o) ⟩
+  (m + m * n) ⊔ (m + m * o)  ≡⟨ cong₂ _⊔_ (*-suc m n) (*-suc m o) ⟨
   (m * suc n) ⊔ (m * suc o)  ∎
 
 *-distribʳ-⊔ : _*_ DistributesOverʳ _⊔_
@@ -1434,20 +1434,20 @@ m⊓n≤m+n m n with ⊓-sel m n
   m * (0 ⊓ o)               ≡⟨⟩
   m * 0                     ≡⟨ *-zeroʳ m ⟩
   0                         ≡⟨⟩
-  0 ⊓ (m * o)               ≡˘⟨ cong (_⊓ (m * o)) (*-zeroʳ m) ⟩
+  0 ⊓ (m * o)               ≡⟨ cong (_⊓ (m * o)) (*-zeroʳ m) ⟨
   (m * 0) ⊓ (m * o)         ∎
 *-distribˡ-⊓ m (suc n) 0 = begin-equality
   m * (suc n ⊓ 0)           ≡⟨⟩
   m * 0                     ≡⟨ *-zeroʳ m ⟩
-  0                         ≡˘⟨ ⊓-zeroʳ (m * suc n) ⟩
-  (m * suc n) ⊓ 0           ≡˘⟨ cong (m * suc n ⊓_) (*-zeroʳ m) ⟩
+  0                         ≡⟨ ⊓-zeroʳ (m * suc n) ⟨
+  (m * suc n) ⊓ 0           ≡⟨ cong (m * suc n ⊓_) (*-zeroʳ m) ⟨
   (m * suc n) ⊓ (m * 0)     ∎
 *-distribˡ-⊓ m (suc n) (suc o) = begin-equality
   m * (suc n ⊓ suc o)       ≡⟨⟩
   m * suc (n ⊓ o)           ≡⟨ *-suc m (n ⊓ o) ⟩
   m + m * (n ⊓ o)           ≡⟨ cong (m +_) (*-distribˡ-⊓ m n o) ⟩
   m + (m * n) ⊓ (m * o)     ≡⟨ +-distribˡ-⊓ m (m * n) (m * o) ⟩
-  (m + m * n) ⊓ (m + m * o) ≡˘⟨ cong₂ _⊓_ (*-suc m n) (*-suc m o) ⟩
+  (m + m * n) ⊓ (m + m * o) ≡⟨ cong₂ _⊓_ (*-suc m n) (*-suc m o) ⟨
   (m * suc n) ⊓ (m * suc o) ∎
 
 *-distribʳ-⊓ : _*_ DistributesOverʳ _⊓_
diff --git a/src/Data/Rational/Properties.agda b/src/Data/Rational/Properties.agda
index 915eb6e058..f0a7d11c96 100644
--- a/src/Data/Rational/Properties.agda
+++ b/src/Data/Rational/Properties.agda
@@ -314,7 +314,7 @@ normalize-injective-≃ m n c d eq = ℕ./-cancelʳ-≡
   (begin
     (m ℕ.* d) ℕ./ (gcd[m,c] ℕ.* gcd[n,d]) ≡⟨  ℕ./-*-interchange gcd[m,c]∣m gcd[n,d]∣d ⟩
     (m ℕ./ gcd[m,c]) ℕ.* (d ℕ./ gcd[n,d]) ≡⟨  cong₂ ℕ._*_ m/gcd[m,c]≡n/gcd[n,d] (sym c/gcd[m,c]≡d/gcd[n,d]) ⟩
-    (n ℕ./ gcd[n,d]) ℕ.* (c ℕ./ gcd[m,c]) ≡˘⟨ ℕ./-*-interchange gcd[n,d]∣n gcd[m,c]∣c ⟩
+    (n ℕ./ gcd[n,d]) ℕ.* (c ℕ./ gcd[m,c]) ≡⟨ ℕ./-*-interchange gcd[n,d]∣n gcd[m,c]∣c ⟨
     (n ℕ.* c) ℕ./ (gcd[n,d] ℕ.* gcd[m,c]) ≡⟨  ℕ./-congʳ (ℕ.*-comm gcd[n,d] gcd[m,c]) ⟩
     (n ℕ.* c) ℕ./ (gcd[m,c] ℕ.* gcd[n,d]) ∎)
   where
@@ -441,7 +441,7 @@ fromℚᵘ-cong : fromℚᵘ Preserves _≃ᵘ_ ⟶ _≡_
 fromℚᵘ-cong {p} {q} p≃q = toℚᵘ-injective (begin-equality
   toℚᵘ (fromℚᵘ p)  ≃⟨  toℚᵘ-fromℚᵘ p ⟩
   p                ≃⟨  p≃q ⟩
-  q                ≃˘⟨ toℚᵘ-fromℚᵘ q ⟩
+  q                ≃⟨ toℚᵘ-fromℚᵘ q ⟨
   toℚᵘ (fromℚᵘ q)  ∎)
   where open ℚᵘ.≤-Reasoning
 
@@ -749,7 +749,8 @@ module ≤-Reasoning where
     ≤-<-trans
     as Triple
 
-  open Triple public hiding (step-≈; step-≈˘)
+  open Triple public
+    hiding (step-≈; step-≈˘; step-≈-⟩; step-≈-⟨)
 
   ≃-go : Trans _≃_ _IsRelatedTo_ _IsRelatedTo_
   ≃-go = Triple.≈-go ∘′ ≃⇒≡
@@ -854,7 +855,7 @@ toℚᵘ-homo-+ p@record{} q@record{} with +-nf p q ℤ.≟ 0ℤ
     ↥ (p + q) ℤ.* +-nf p q ℤ.* ↧+ᵘ p q            ≡⟨ cong (ℤ._* ↧+ᵘ p q) (↥-+ p q) ⟩
     ↥+ᵘ p q ℤ.* ↧+ᵘ p q                           ≡⟨ cong (↥+ᵘ p q ℤ.*_) (sym (↧-+ p q)) ⟩
     ↥+ᵘ p q ℤ.* (↧ (p + q) ℤ.* +-nf p q)          ≡⟨ x∙yz≈xy∙z (↥+ᵘ p q) _ _ ⟩
-    ↥+ᵘ p q ℤ.* ↧ (p + q)  ℤ.* +-nf p q           ≡˘⟨ cong (λ v → ↥+ᵘ p q ℤ.* v ℤ.* +-nf p q) (↧ᵘ-toℚᵘ (p + q)) ⟩
+    ↥+ᵘ p q ℤ.* ↧ (p + q)  ℤ.* +-nf p q           ≡⟨ cong (λ v → ↥+ᵘ p q ℤ.* v ℤ.* +-nf p q) (↧ᵘ-toℚᵘ (p + q)) ⟨
     ↥+ᵘ p q ℤ.* ↧ᵘ (toℚᵘ (p + q)) ℤ.* +-nf p q    ∎)
   where open ≡-Reasoning; open CommSemigroupProperties ℤ.*-commutativeSemigroup
 
@@ -1065,7 +1066,7 @@ toℚᵘ-homo-* p@record{} q@record{} with *-nf p q ℤ.≟ 0ℤ
   ↥ (p * q)         ℤ.* *-nf p q ℤ.* (↧ p ℤ.* ↧ q)     ≡⟨ cong (ℤ._* (↧ p ℤ.* ↧ q)) (↥-* p q) ⟩
   (↥ p ℤ.* ↥ q)     ℤ.* (↧ p ℤ.* ↧ q)                  ≡⟨ cong ((↥ p ℤ.* ↥ q) ℤ.*_) (sym (↧-* p q)) ⟩
   (↥ p ℤ.* ↥ q)     ℤ.* (↧ (p * q) ℤ.* *-nf p q)       ≡⟨ x∙yz≈xy∙z (↥ p ℤ.* ↥ q) _ _ ⟩
-  (↥ p ℤ.* ↥ q)     ℤ.* ↧ (p * q)  ℤ.* *-nf p q        ≡˘⟨ cong (λ v → (↥ p ℤ.* ↥ q) ℤ.* v ℤ.* *-nf p q) (↧ᵘ-toℚᵘ (p * q)) ⟩
+  (↥ p ℤ.* ↥ q)     ℤ.* ↧ (p * q)  ℤ.* *-nf p q        ≡⟨ cong (λ v → (↥ p ℤ.* ↥ q) ℤ.* v ℤ.* *-nf p q) (↧ᵘ-toℚᵘ (p * q)) ⟨
   (↥ p ℤ.* ↥ q)     ℤ.* ↧ᵘ (toℚᵘ (p * q)) ℤ.* *-nf p q ∎)
   where open ≡-Reasoning; open CommSemigroupProperties ℤ.*-commutativeSemigroup
 
@@ -1242,7 +1243,7 @@ neg-distribʳ-* = +-*-Monomorphism.neg-distribʳ-* ℚᵘ.+-0-isGroup ℚᵘ.*-i
 
 *-cancelʳ-≤-pos : ∀ r .{{_ : Positive r}} → p * r ≤ q * r → p ≤ q
 *-cancelʳ-≤-pos {p} {q} r pr≤qr = toℚᵘ-cancel-≤ (ℚᵘ.*-cancelʳ-≤-pos (toℚᵘ r) (begin
-  toℚᵘ p ℚᵘ.* toℚᵘ r  ≃˘⟨ toℚᵘ-homo-* p r ⟩
+  toℚᵘ p ℚᵘ.* toℚᵘ r  ≃⟨ toℚᵘ-homo-* p r ⟨
   toℚᵘ (p * r)        ≤⟨  toℚᵘ-mono-≤ pr≤qr ⟩
   toℚᵘ (q * r)        ≃⟨  toℚᵘ-homo-* q r ⟩
   toℚᵘ q ℚᵘ.* toℚᵘ r  ∎))
@@ -1255,7 +1256,7 @@ neg-distribʳ-* = +-*-Monomorphism.neg-distribʳ-* ℚᵘ.+-0-isGroup ℚᵘ.*-i
 *-monoʳ-≤-nonNeg r {p} {q} p≤q = toℚᵘ-cancel-≤ (begin
   toℚᵘ (p * r)        ≃⟨  toℚᵘ-homo-* p r ⟩
   toℚᵘ p ℚᵘ.* toℚᵘ r  ≤⟨  ℚᵘ.*-monoˡ-≤-nonNeg (toℚᵘ r) (toℚᵘ-mono-≤ p≤q) ⟩
-  toℚᵘ q ℚᵘ.* toℚᵘ r  ≃˘⟨ toℚᵘ-homo-* q r ⟩
+  toℚᵘ q ℚᵘ.* toℚᵘ r  ≃⟨ toℚᵘ-homo-* q r ⟨
   toℚᵘ (q * r)        ∎)
   where open ℚᵘ.≤-Reasoning
 
@@ -1266,7 +1267,7 @@ neg-distribʳ-* = +-*-Monomorphism.neg-distribʳ-* ℚᵘ.+-0-isGroup ℚᵘ.*-i
 *-monoʳ-≤-nonPos r {p} {q} p≤q = toℚᵘ-cancel-≤ (begin
   toℚᵘ (q * r)        ≃⟨ toℚᵘ-homo-* q r ⟩
   toℚᵘ q ℚᵘ.* toℚᵘ r  ≤⟨ ℚᵘ.*-monoˡ-≤-nonPos (toℚᵘ r) (toℚᵘ-mono-≤ p≤q) ⟩
-  toℚᵘ p ℚᵘ.* toℚᵘ r  ≃˘⟨ toℚᵘ-homo-* p r ⟩
+  toℚᵘ p ℚᵘ.* toℚᵘ r  ≃⟨ toℚᵘ-homo-* p r ⟨
   toℚᵘ (p * r)        ∎)
   where open ℚᵘ.≤-Reasoning
 
@@ -1275,9 +1276,9 @@ neg-distribʳ-* = +-*-Monomorphism.neg-distribʳ-* ℚᵘ.+-0-isGroup ℚᵘ.*-i
 
 *-cancelʳ-≤-neg : ∀ r .{{_ : Negative r}} → p * r ≤ q * r → p ≥ q
 *-cancelʳ-≤-neg {p} {q} r pr≤qr = toℚᵘ-cancel-≤ (ℚᵘ.*-cancelʳ-≤-neg _ (begin
-  toℚᵘ p ℚᵘ.* toℚᵘ r  ≃˘⟨ toℚᵘ-homo-* p r ⟩
-  toℚᵘ (p * r)        ≤⟨  toℚᵘ-mono-≤ pr≤qr ⟩
-  toℚᵘ (q * r)        ≃⟨  toℚᵘ-homo-* q r ⟩
+  toℚᵘ p ℚᵘ.* toℚᵘ r  ≃⟨ toℚᵘ-homo-* p r ⟨
+  toℚᵘ (p * r)        ≤⟨ toℚᵘ-mono-≤ pr≤qr ⟩
+  toℚᵘ (q * r)        ≃⟨ toℚᵘ-homo-* q r ⟩
   toℚᵘ q ℚᵘ.* toℚᵘ r  ∎))
   where open ℚᵘ.≤-Reasoning
 
@@ -1291,7 +1292,7 @@ neg-distribʳ-* = +-*-Monomorphism.neg-distribʳ-* ℚᵘ.+-0-isGroup ℚᵘ.*-i
 *-monoˡ-<-pos r {p} {q} p<q = toℚᵘ-cancel-< (begin-strict
   toℚᵘ (p * r)        ≃⟨ toℚᵘ-homo-* p r ⟩
   toℚᵘ p ℚᵘ.* toℚᵘ r  <⟨ ℚᵘ.*-monoˡ-<-pos (toℚᵘ r) (toℚᵘ-mono-< p<q) ⟩
-  toℚᵘ q ℚᵘ.* toℚᵘ r  ≃˘⟨ toℚᵘ-homo-* q r ⟩
+  toℚᵘ q ℚᵘ.* toℚᵘ r  ≃⟨ toℚᵘ-homo-* q r ⟨
   toℚᵘ (q * r)        ∎)
   where open ℚᵘ.≤-Reasoning
 
@@ -1300,7 +1301,7 @@ neg-distribʳ-* = +-*-Monomorphism.neg-distribʳ-* ℚᵘ.+-0-isGroup ℚᵘ.*-i
 
 *-cancelˡ-<-nonNeg : ∀ r .{{_ : NonNegative r}} → ∀ {p q} → r * p < r * q → p < q
 *-cancelˡ-<-nonNeg r {p} {q} rp<rq = toℚᵘ-cancel-< (ℚᵘ.*-cancelˡ-<-nonNeg (toℚᵘ r) (begin-strict
-  toℚᵘ r ℚᵘ.* toℚᵘ p  ≃˘⟨ toℚᵘ-homo-* r p ⟩
+  toℚᵘ r ℚᵘ.* toℚᵘ p  ≃⟨ toℚᵘ-homo-* r p ⟨
   toℚᵘ (r * p)        <⟨ toℚᵘ-mono-< rp<rq ⟩
   toℚᵘ (r * q)        ≃⟨ toℚᵘ-homo-* r q ⟩
   toℚᵘ r ℚᵘ.* toℚᵘ q  ∎))
@@ -1313,7 +1314,7 @@ neg-distribʳ-* = +-*-Monomorphism.neg-distribʳ-* ℚᵘ.+-0-isGroup ℚᵘ.*-i
 *-monoˡ-<-neg r {p} {q} p<q = toℚᵘ-cancel-< (begin-strict
   toℚᵘ (q * r)        ≃⟨ toℚᵘ-homo-* q r ⟩
   toℚᵘ q ℚᵘ.* toℚᵘ r  <⟨ ℚᵘ.*-monoˡ-<-neg (toℚᵘ r) (toℚᵘ-mono-< p<q) ⟩
-  toℚᵘ p ℚᵘ.* toℚᵘ r  ≃˘⟨ toℚᵘ-homo-* p r ⟩
+  toℚᵘ p ℚᵘ.* toℚᵘ r  ≃⟨ toℚᵘ-homo-* p r ⟨
   toℚᵘ (p * r)        ∎)
   where open ℚᵘ.≤-Reasoning
 
@@ -1322,7 +1323,7 @@ neg-distribʳ-* = +-*-Monomorphism.neg-distribʳ-* ℚᵘ.+-0-isGroup ℚᵘ.*-i
 
 *-cancelˡ-<-nonPos : ∀ r .{{_ : NonPositive r}} → r * p < r * q → p > q
 *-cancelˡ-<-nonPos {p} {q} r rp<rq = toℚᵘ-cancel-< (ℚᵘ.*-cancelˡ-<-nonPos (toℚᵘ r) (begin-strict
-  toℚᵘ r ℚᵘ.* toℚᵘ p  ≃˘⟨ toℚᵘ-homo-* r p ⟩
+  toℚᵘ r ℚᵘ.* toℚᵘ p  ≃⟨ toℚᵘ-homo-* r p ⟨
   toℚᵘ (r * p)        <⟨  toℚᵘ-mono-< rp<rq ⟩
   toℚᵘ (r * q)        ≃⟨  toℚᵘ-homo-* r q ⟩
   toℚᵘ r ℚᵘ.* toℚᵘ q  ∎))
@@ -1488,17 +1489,17 @@ mono-<-distrib-⊓ : ∀ {f} → f Preserves _<_ ⟶ _<_ →
 mono-<-distrib-⊓ {f} f-mono-< p q with <-cmp p q
 ... | tri< p<q p≢r  p≯q = begin
   f (p ⊓ q)  ≡⟨ cong f (p≤q⇒p⊓q≡p (<⇒≤ p<q)) ⟩
-  f p        ≡˘⟨ p≤q⇒p⊓q≡p (<⇒≤ (f-mono-< p<q)) ⟩
+  f p        ≡⟨ p≤q⇒p⊓q≡p (<⇒≤ (f-mono-< p<q)) ⟨
   f p ⊓ f q  ∎
   where open ≡-Reasoning
 ... | tri≈ p≮q refl p≯q = begin
   f (p ⊓ q)  ≡⟨ cong f (⊓-idem p) ⟩
-  f p        ≡˘⟨ ⊓-idem (f p) ⟩
+  f p        ≡⟨ ⊓-idem (f p) ⟨
   f p ⊓ f q  ∎
   where open ≡-Reasoning
 ... | tri> p≮q p≡r  p>q = begin
   f (p ⊓ q)  ≡⟨ cong f (p≥q⇒p⊓q≡q (<⇒≤ p>q)) ⟩
-  f q        ≡˘⟨ p≥q⇒p⊓q≡q (<⇒≤ (f-mono-< p>q)) ⟩
+  f q        ≡⟨ p≥q⇒p⊓q≡q (<⇒≤ (f-mono-< p>q)) ⟨
   f p ⊓ f q  ∎
   where open ≡-Reasoning
 
@@ -1507,17 +1508,17 @@ mono-<-distrib-⊔ : ∀ {f} → f Preserves _<_ ⟶ _<_ →
 mono-<-distrib-⊔ {f} f-mono-< p q with <-cmp p q
 ... | tri< p<q p≢r  p≯q = begin
   f (p ⊔ q)  ≡⟨ cong f (p≤q⇒p⊔q≡q (<⇒≤ p<q)) ⟩
-  f q        ≡˘⟨ p≤q⇒p⊔q≡q (<⇒≤ (f-mono-< p<q)) ⟩
+  f q        ≡⟨ p≤q⇒p⊔q≡q (<⇒≤ (f-mono-< p<q)) ⟨
   f p ⊔ f q  ∎
   where open ≡-Reasoning
 ... | tri≈ p≮q refl p≯q = begin
   f (p ⊔ q)  ≡⟨ cong f (⊔-idem p) ⟩
-  f q        ≡˘⟨ ⊔-idem (f p) ⟩
+  f q        ≡⟨ ⊔-idem (f p) ⟨
   f p ⊔ f q  ∎
   where open ≡-Reasoning
 ... | tri> p≮q p≡r  p>q = begin
   f (p ⊔ q)  ≡⟨ cong f (p≥q⇒p⊔q≡p (<⇒≤ p>q)) ⟩
-  f p        ≡˘⟨ p≥q⇒p⊔q≡p (<⇒≤ (f-mono-< p>q)) ⟩
+  f p        ≡⟨ p≥q⇒p⊔q≡p (<⇒≤ (f-mono-< p>q)) ⟨
   f p ⊔ f q  ∎
   where open ≡-Reasoning
 
@@ -1605,7 +1606,7 @@ toℚᵘ-homo-∣-∣ (mkℚ -[1+ _ ] _ _) = *≡* refl
 0≤∣p∣ p@record{} = *≤* (begin
   (↥ 0ℚ) ℤ.* (↧ ∣ p ∣)  ≡⟨ ℤ.*-zeroˡ (↧ ∣ p ∣) ⟩
   0ℤ                    ≤⟨ ℤ.+≤+ ℕ.z≤n ⟩
-  ↥ ∣ p ∣               ≡˘⟨ ℤ.*-identityʳ (↥ ∣ p ∣) ⟩
+  ↥ ∣ p ∣               ≡⟨ ℤ.*-identityʳ (↥ ∣ p ∣) ⟨
   ↥ ∣ p ∣ ℤ.* 1ℤ        ∎)
   where open ℤ.≤-Reasoning
 
@@ -1633,8 +1634,8 @@ toℚᵘ-homo-∣-∣ (mkℚ -[1+ _ ] _ _) = *≡* refl
   toℚᵘ ∣ p + q ∣                    ≃⟨ toℚᵘ-homo-∣-∣ (p + q) ⟩
   ℚᵘ.∣ toℚᵘ (p + q) ∣               ≃⟨ ℚᵘ.∣-∣-cong (toℚᵘ-homo-+ p q) ⟩
   ℚᵘ.∣ toℚᵘ p ℚᵘ.+ toℚᵘ q ∣         ≤⟨ ℚᵘ.∣p+q∣≤∣p∣+∣q∣ (toℚᵘ p) (toℚᵘ q) ⟩
-  ℚᵘ.∣ toℚᵘ p ∣ ℚᵘ.+ ℚᵘ.∣ toℚᵘ q ∣  ≃˘⟨ ℚᵘ.+-cong (toℚᵘ-homo-∣-∣ p) (toℚᵘ-homo-∣-∣ q) ⟩
-  toℚᵘ ∣ p ∣ ℚᵘ.+ toℚᵘ ∣ q ∣        ≃˘⟨ toℚᵘ-homo-+ ∣ p ∣ ∣ q ∣ ⟩
+  ℚᵘ.∣ toℚᵘ p ∣ ℚᵘ.+ ℚᵘ.∣ toℚᵘ q ∣  ≃⟨ ℚᵘ.+-cong (toℚᵘ-homo-∣-∣ p) (toℚᵘ-homo-∣-∣ q) ⟨
+  toℚᵘ ∣ p ∣ ℚᵘ.+ toℚᵘ ∣ q ∣        ≃⟨ toℚᵘ-homo-+ ∣ p ∣ ∣ q ∣ ⟨
   toℚᵘ (∣ p ∣ + ∣ q ∣)              ∎)
   where open ℚᵘ.≤-Reasoning
 
@@ -1650,8 +1651,8 @@ toℚᵘ-homo-∣-∣ (mkℚ -[1+ _ ] _ _) = *≡* refl
   toℚᵘ ∣ p * q ∣                    ≃⟨ toℚᵘ-homo-∣-∣ (p * q) ⟩
   ℚᵘ.∣ toℚᵘ (p * q) ∣               ≃⟨ ℚᵘ.∣-∣-cong (toℚᵘ-homo-* p q) ⟩
   ℚᵘ.∣ toℚᵘ p ℚᵘ.* toℚᵘ q ∣         ≃⟨ ℚᵘ.∣p*q∣≃∣p∣*∣q∣ (toℚᵘ p) (toℚᵘ q) ⟩
-  ℚᵘ.∣ toℚᵘ p ∣ ℚᵘ.* ℚᵘ.∣ toℚᵘ q ∣  ≃˘⟨ ℚᵘ.*-cong (toℚᵘ-homo-∣-∣ p) (toℚᵘ-homo-∣-∣ q) ⟩
-  toℚᵘ ∣ p ∣ ℚᵘ.* toℚᵘ ∣ q ∣        ≃˘⟨ toℚᵘ-homo-* ∣ p ∣ ∣ q ∣ ⟩
+  ℚᵘ.∣ toℚᵘ p ∣ ℚᵘ.* ℚᵘ.∣ toℚᵘ q ∣  ≃⟨ ℚᵘ.*-cong (toℚᵘ-homo-∣-∣ p) (toℚᵘ-homo-∣-∣ q) ⟨
+  toℚᵘ ∣ p ∣ ℚᵘ.* toℚᵘ ∣ q ∣        ≃⟨ toℚᵘ-homo-* ∣ p ∣ ∣ q ∣ ⟨
   toℚᵘ (∣ p ∣ * ∣ q ∣)              ∎)
   where open ℚᵘ.≤-Reasoning
 
diff --git a/src/Data/Rational/Unnormalised/Properties.agda b/src/Data/Rational/Unnormalised/Properties.agda
index 6348a6ef46..dce11c3f21 100644
--- a/src/Data/Rational/Unnormalised/Properties.agda
+++ b/src/Data/Rational/Unnormalised/Properties.agda
@@ -160,7 +160,7 @@ module ≃-Reasoning = SetoidReasoning ≃-setoid
 
 p≃0⇒↥p≡0 : ∀ p → p ≃ 0ℚᵘ → ↥ p ≡ 0ℤ
 p≃0⇒↥p≡0 p (*≡* eq) = begin
-  ↥ p          ≡˘⟨ ℤ.*-identityʳ (↥ p) ⟩
+  ↥ p          ≡⟨ ℤ.*-identityʳ (↥ p) ⟨
   ↥ p ℤ.* 1ℤ  ≡⟨ eq ⟩
   0ℤ           ∎
   where open ≡-Reasoning
@@ -180,14 +180,14 @@ neg-involutive p rewrite neg-involutive-≡ p = ≃-refl
 
 -‿cong : Congruent₁ _≃_ (-_)
 -‿cong {p@record{}} {q@record{}} (*≡* p≡q) = *≡* (begin
-  ↥(- p) ℤ.* ↧ q            ≡˘⟨ ℤ.*-identityˡ (ℤ.- (↥ p) ℤ.* ↧ q) ⟩
-  1ℤ ℤ.* (↥(- p) ℤ.* ↧ q)   ≡˘⟨ ℤ.*-assoc 1ℤ (↥ (- p)) (↧ q) ⟩
-  (1ℤ ℤ.* ℤ.-(↥ p)) ℤ.* ↧ q ≡˘⟨ cong (ℤ._* ↧ q) (ℤ.neg-distribʳ-* 1ℤ (↥ p)) ⟩
+  ↥(- p) ℤ.* ↧ q            ≡⟨ ℤ.*-identityˡ (ℤ.- (↥ p) ℤ.* ↧ q) ⟨
+  1ℤ ℤ.* (↥(- p) ℤ.* ↧ q)   ≡⟨ ℤ.*-assoc 1ℤ (↥ (- p)) (↧ q) ⟨
+  (1ℤ ℤ.* ℤ.-(↥ p)) ℤ.* ↧ q ≡⟨ cong (ℤ._* ↧ q) (ℤ.neg-distribʳ-* 1ℤ (↥ p)) ⟨
   ℤ.-(1ℤ ℤ.* ↥ p) ℤ.* ↧ q   ≡⟨  cong (ℤ._* ↧ q) (ℤ.neg-distribˡ-* 1ℤ (↥ p)) ⟩
   (-1ℤ ℤ.* ↥ p) ℤ.* ↧ q     ≡⟨  ℤ.*-assoc ℤ.-1ℤ (↥ p) (↧ q) ⟩
   -1ℤ ℤ.* (↥ p ℤ.* ↧ q)     ≡⟨  cong (ℤ.-1ℤ ℤ.*_) p≡q ⟩
-  -1ℤ ℤ.* (↥ q ℤ.* ↧ p)     ≡˘⟨ ℤ.*-assoc ℤ.-1ℤ (↥ q) (↧ p) ⟩
-  (-1ℤ ℤ.* ↥ q) ℤ.* ↧ p     ≡˘⟨ cong (ℤ._* ↧ p) (ℤ.neg-distribˡ-* 1ℤ (↥ q)) ⟩
+  -1ℤ ℤ.* (↥ q ℤ.* ↧ p)     ≡⟨ ℤ.*-assoc ℤ.-1ℤ (↥ q) (↧ p) ⟨
+  (-1ℤ ℤ.* ↥ q) ℤ.* ↧ p     ≡⟨ cong (ℤ._* ↧ p) (ℤ.neg-distribˡ-* 1ℤ (↥ q)) ⟨
   ℤ.-(1ℤ ℤ.* ↥ q) ℤ.* ↧ p   ≡⟨  cong (ℤ._* ↧ p) (ℤ.neg-distribʳ-* 1ℤ (↥ q)) ⟩
   (1ℤ ℤ.* ↥(- q)) ℤ.* ↧ p   ≡⟨  ℤ.*-assoc 1ℤ (ℤ.- (↥ q)) (↧ p) ⟩
   1ℤ ℤ.* (↥(- q) ℤ.* ↧ p)   ≡⟨  ℤ.*-identityˡ (↥ (- q) ℤ.* ↧ p) ⟩
@@ -196,7 +196,7 @@ neg-involutive p rewrite neg-involutive-≡ p = ≃-refl
 
 neg-mono-< : -_ Preserves  _<_ ⟶ _>_
 neg-mono-< {p@record{}} {q@record{}} (*<* p<q) = *<* $ begin-strict
-  ℤ.-  ↥ q ℤ.* ↧ p     ≡˘⟨ ℤ.neg-distribˡ-* (↥ q) (↧ p) ⟩
+  ℤ.-  ↥ q ℤ.* ↧ p     ≡⟨ ℤ.neg-distribˡ-* (↥ q) (↧ p) ⟨
   ℤ.- (↥ q ℤ.* ↧ p)    <⟨ ℤ.neg-mono-< p<q ⟩
   ℤ.- (↥ p ℤ.* ↧ q)    ≡⟨ ℤ.neg-distribˡ-* (↥ p) (↧ q) ⟩
   ↥ (- p) ℤ.* ↧ (- q)  ∎
@@ -204,10 +204,10 @@ neg-mono-< {p@record{}} {q@record{}} (*<* p<q) = *<* $ begin-strict
 
 neg-cancel-< : ∀ {p q} → - p < - q → q < p
 neg-cancel-< {p@record{}} {q@record{}} (*<* -↥p↧q<-↥q↧p) = *<* $ begin-strict
-  ↥ q ℤ.* ↧ p              ≡˘⟨ ℤ.neg-involutive (↥ q ℤ.* ↧ p) ⟩
+  ↥ q ℤ.* ↧ p              ≡⟨ ℤ.neg-involutive (↥ q ℤ.* ↧ p) ⟨
   ℤ.- ℤ.- (↥ q ℤ.* ↧ p)    ≡⟨ cong ℤ.-_ (ℤ.neg-distribˡ-* (↥ q) (↧ p)) ⟩
   ℤ.- ((ℤ.- ↥ q) ℤ.* ↧ p)  <⟨ ℤ.neg-mono-< -↥p↧q<-↥q↧p ⟩
-  ℤ.- ((ℤ.- ↥ p) ℤ.* ↧ q)  ≡˘⟨ cong ℤ.-_ (ℤ.neg-distribˡ-* (↥ p) (↧ q)) ⟩
+  ℤ.- ((ℤ.- ↥ p) ℤ.* ↧ q)  ≡⟨ cong ℤ.-_ (ℤ.neg-distribˡ-* (↥ p) (↧ q)) ⟨
   ℤ.- ℤ.- (↥ p ℤ.* ↧ q)    ≡⟨ ℤ.neg-involutive (↥ p ℤ.* ↧ q) ⟩
   ↥ p ℤ.* ↧ q              ∎
   where open ℤ.≤-Reasoning
@@ -235,12 +235,12 @@ drop-*≤* (*≤* pq≤qp) = pq≤qp
   ℤ.*-cancelʳ-≤-pos (n₁ ℤ.* d₃) (n₃ ℤ.* d₁) d₂ $ begin
   (n₁  ℤ.* d₃) ℤ.* d₂  ≡⟨ ℤ.*-assoc n₁ d₃ d₂ ⟩
   n₁   ℤ.* (d₃ ℤ.* d₂) ≡⟨ cong (n₁ ℤ.*_) (ℤ.*-comm d₃ d₂) ⟩
-  n₁   ℤ.* (d₂ ℤ.* d₃) ≡˘⟨ ℤ.*-assoc n₁ d₂ d₃ ⟩
+  n₁   ℤ.* (d₂ ℤ.* d₃) ≡⟨ ℤ.*-assoc n₁ d₂ d₃ ⟨
   (n₁  ℤ.* d₂) ℤ.* d₃  ≤⟨ ℤ.*-monoʳ-≤-nonNeg d₃ eq₁ ⟩
   (n₂  ℤ.* d₁) ℤ.* d₃  ≡⟨ cong (ℤ._* d₃) (ℤ.*-comm n₂ d₁) ⟩
   (d₁ ℤ.* n₂)  ℤ.* d₃  ≡⟨ ℤ.*-assoc d₁ n₂ d₃ ⟩
   d₁  ℤ.* (n₂  ℤ.* d₃) ≤⟨ ℤ.*-monoˡ-≤-nonNeg d₁ eq₂ ⟩
-  d₁  ℤ.* (n₃  ℤ.* d₂) ≡˘⟨ ℤ.*-assoc d₁ n₃ d₂ ⟩
+  d₁  ℤ.* (n₃  ℤ.* d₂) ≡⟨ ℤ.*-assoc d₁ n₃ d₂ ⟨
   (d₁ ℤ.* n₃)  ℤ.* d₂  ≡⟨ cong (ℤ._* d₂) (ℤ.*-comm d₁ n₃) ⟩
   (n₃  ℤ.* d₁) ℤ.* d₂  ∎ where open ℤ.≤-Reasoning
 
@@ -439,7 +439,7 @@ drop-*<* (*<* pq<qp) = pq<qp
     ↥ p ℤ.* ↧ p ℤ.+ ↥ p ℤ.* ↧ q
       <⟨ ℤ.+-monoʳ-< (↥ p ℤ.* ↧ p) p<q ⟩
     ↥ p ℤ.* ↧ p ℤ.+ ↥ q ℤ.* ↧ p
-      ≡˘⟨ ℤ.*-distribʳ-+ (↧ p) (↥ p) (↥ q) ⟩
+      ≡⟨ ℤ.*-distribʳ-+ (↧ p) (↥ p) (↥ q) ⟨
     (↥ p ℤ.+ ↥ q) ℤ.* ↧ p
       ≡⟨⟩
     ↥ m ℤ.* ↧ p ∎)
@@ -451,7 +451,7 @@ drop-*<* (*<* pq<qp) = pq<qp
     ↥ p ℤ.* ↧ q ℤ.+ ↥ q ℤ.* ↧ q
       <⟨ ℤ.+-monoˡ-< (↥ q ℤ.* ↧ q) p<q ⟩
     ↥ q ℤ.* ↧ p ℤ.+ ↥ q ℤ.* ↧ q
-      ≡˘⟨ ℤ.*-distribˡ-+ (↥ q) (↧ p) (↧ q) ⟩
+      ≡⟨ ℤ.*-distribˡ-+ (↥ q) (↧ p) (↧ q) ⟨
     ↥ q ℤ.* (↧ p ℤ.+ ↧ q)
       ≡⟨⟩
     ↥ q ℤ.* ↧ m ∎)
@@ -461,12 +461,12 @@ drop-*<* (*<* pq<qp) = pq<qp
   ℤ.*-cancelʳ-<-nonNeg _ $ begin-strict
   n₁ ℤ.*  d₃ ℤ.* d₂  ≡⟨ ℤ.*-assoc n₁ d₃ d₂ ⟩
   n₁ ℤ.* (d₃ ℤ.* d₂) ≡⟨ cong (n₁ ℤ.*_) (ℤ.*-comm d₃ d₂) ⟩
-  n₁ ℤ.* (d₂ ℤ.* d₃) ≡˘⟨ ℤ.*-assoc n₁ d₂ d₃ ⟩
+  n₁ ℤ.* (d₂ ℤ.* d₃) ≡⟨ ℤ.*-assoc n₁ d₂ d₃ ⟨
   n₁ ℤ.*  d₂ ℤ.* d₃  ≤⟨ ℤ.*-monoʳ-≤-nonNeg (↧ r) p≤q ⟩
   n₂ ℤ.*  d₁ ℤ.* d₃  ≡⟨ cong (ℤ._* d₃) (ℤ.*-comm n₂ d₁) ⟩
   d₁ ℤ.*  n₂ ℤ.* d₃  ≡⟨ ℤ.*-assoc d₁ n₂ d₃ ⟩
   d₁ ℤ.* (n₂ ℤ.* d₃) <⟨ ℤ.*-monoˡ-<-pos (↧ p) q<r ⟩
-  d₁ ℤ.* (n₃ ℤ.* d₂) ≡˘⟨ ℤ.*-assoc d₁ n₃ d₂ ⟩
+  d₁ ℤ.* (n₃ ℤ.* d₂) ≡⟨ ℤ.*-assoc d₁ n₃ d₂ ⟨
   d₁ ℤ.*  n₃ ℤ.* d₂  ≡⟨ cong (ℤ._* d₂) (ℤ.*-comm d₁ n₃) ⟩
   n₃ ℤ.*  d₁ ℤ.* d₂  ∎
   where open ℤ.≤-Reasoning
@@ -477,12 +477,12 @@ drop-*<* (*<* pq<qp) = pq<qp
   ℤ.*-cancelʳ-<-nonNeg _ $ begin-strict
   n₁ ℤ.*  d₃ ℤ.* d₂  ≡⟨ ℤ.*-assoc n₁ d₃ d₂ ⟩
   n₁ ℤ.* (d₃ ℤ.* d₂) ≡⟨ cong (n₁ ℤ.*_) (ℤ.*-comm d₃ d₂) ⟩
-  n₁ ℤ.* (d₂ ℤ.* d₃) ≡˘⟨ ℤ.*-assoc n₁ d₂ d₃ ⟩
+  n₁ ℤ.* (d₂ ℤ.* d₃) ≡⟨ ℤ.*-assoc n₁ d₂ d₃ ⟨
   n₁ ℤ.*  d₂ ℤ.* d₃  <⟨ ℤ.*-monoʳ-<-pos (↧ r) p<q ⟩
   n₂ ℤ.*  d₁ ℤ.* d₃  ≡⟨ cong (ℤ._* d₃) (ℤ.*-comm n₂ d₁) ⟩
   d₁ ℤ.*  n₂ ℤ.* d₃  ≡⟨ ℤ.*-assoc d₁ n₂ d₃ ⟩
   d₁ ℤ.* (n₂ ℤ.* d₃) ≤⟨ ℤ.*-monoˡ-≤-nonNeg (↧ p) q≤r ⟩
-  d₁ ℤ.* (n₃ ℤ.* d₂) ≡˘⟨ ℤ.*-assoc d₁ n₃ d₂ ⟩
+  d₁ ℤ.* (n₃ ℤ.* d₂) ≡⟨ ℤ.*-assoc d₁ n₃ d₂ ⟨
   d₁ ℤ.*  n₃ ℤ.* d₂  ≡⟨ cong (ℤ._* d₂) (ℤ.*-comm d₁ n₃) ⟩
   n₃ ℤ.*  d₁ ℤ.* d₂  ∎
   where open ℤ.≤-Reasoning
@@ -513,15 +513,15 @@ _>?_ = flip _<?_
   ℤ.*-cancelʳ-<-nonNeg _ $ begin-strict
   n₁ ℤ.*  d₃ ℤ.* d₂  ≡⟨ ℤ.*-assoc n₁ d₃ d₂ ⟩
   n₁ ℤ.* (d₃ ℤ.* d₂) ≡⟨ cong (n₁ ℤ.*_) (ℤ.*-comm d₃ d₂) ⟩
-  n₁ ℤ.* (d₂ ℤ.* d₃) ≡˘⟨ ℤ.*-assoc n₁ d₂ d₃ ⟩
+  n₁ ℤ.* (d₂ ℤ.* d₃) ≡⟨ ℤ.*-assoc n₁ d₂ d₃ ⟨
   n₁ ℤ.*  d₂ ℤ.* d₃  <⟨ ℤ.*-monoʳ-<-pos (↧ r) p<q ⟩
   n₂ ℤ.*  d₁ ℤ.* d₃  ≡⟨ ℤ.*-assoc n₂ d₁ d₃ ⟩
   n₂ ℤ.* (d₁ ℤ.* d₃) ≡⟨ cong (n₂ ℤ.*_) (ℤ.*-comm d₁ d₃) ⟩
-  n₂ ℤ.* (d₃ ℤ.* d₁) ≡˘⟨ ℤ.*-assoc n₂ d₃ d₁ ⟩
+  n₂ ℤ.* (d₃ ℤ.* d₁) ≡⟨ ℤ.*-assoc n₂ d₃ d₁ ⟨
   n₂ ℤ.*  d₃ ℤ.* d₁  ≡⟨ cong (ℤ._* d₁) q≡r ⟩
   n₃ ℤ.*  d₂ ℤ.* d₁  ≡⟨ ℤ.*-assoc n₃ d₂ d₁ ⟩
   n₃ ℤ.* (d₂ ℤ.* d₁) ≡⟨ cong (n₃ ℤ.*_) (ℤ.*-comm d₂ d₁) ⟩
-  n₃ ℤ.* (d₁ ℤ.* d₂) ≡˘⟨ ℤ.*-assoc n₃ d₁ d₂ ⟩
+  n₃ ℤ.* (d₁ ℤ.* d₂) ≡⟨ ℤ.*-assoc n₃ d₁ d₂ ⟨
   n₃ ℤ.*  d₁ ℤ.* d₂  ∎
   where open ℤ.≤-Reasoning
         n₁ = ↥ p; n₂ = ↥ q; n₃ = ↥ r; d₁ = ↧ p; d₂ = ↧ q; d₃ = ↧ r
@@ -605,9 +605,10 @@ module ≤-Reasoning where
     as Triple
 
   open Triple public
-    hiding (step-≈; step-≈˘)
+    hiding (step-≈; step-≈˘; step-≈-⟩; step-≈-⟨)
+    renaming (≈-go to ≃-go)
 
-  open ≃-syntax _IsRelatedTo_ _IsRelatedTo_  Triple.≈-go ≃-sym public
+  open ≃-syntax _IsRelatedTo_ _IsRelatedTo_ ≃-go ≃-sym public
 
 ------------------------------------------------------------------------
 -- Properties of ↥_/↧_
@@ -760,14 +761,14 @@ neg⇒nonZero (mkℚᵘ (-[1+ _ ]) _) = _
 +-inverseˡ : LeftInverse _≃_ 0ℚᵘ -_ _+_
 +-inverseˡ p@record{} = *≡* let n = ↥ p; d = ↧ p in
   ((ℤ.- n) ℤ.* d ℤ.+ n ℤ.* d) ℤ.* 1ℤ ≡⟨ ℤ.*-identityʳ ((ℤ.- n) ℤ.* d ℤ.+ n ℤ.* d) ⟩
-  (ℤ.- n) ℤ.* d ℤ.+ n ℤ.* d          ≡˘⟨ cong (ℤ._+ (n ℤ.* d)) (ℤ.neg-distribˡ-* n d) ⟩
+  (ℤ.- n) ℤ.* d ℤ.+ n ℤ.* d          ≡⟨ cong (ℤ._+ (n ℤ.* d)) (ℤ.neg-distribˡ-* n d) ⟨
   ℤ.- (n ℤ.* d) ℤ.+ n ℤ.* d          ≡⟨ ℤ.+-inverseˡ (n ℤ.* d) ⟩
   0ℤ                                 ∎ where open ≡-Reasoning
 
 +-inverseʳ : RightInverse _≃_ 0ℚᵘ -_ _+_
 +-inverseʳ p@record{} = *≡* let n = ↥ p; d = ↧ p in
   (n ℤ.* d ℤ.+ (ℤ.- n) ℤ.* d) ℤ.* 1ℤ ≡⟨ ℤ.*-identityʳ (n ℤ.* d ℤ.+ (ℤ.- n) ℤ.* d) ⟩
-  n ℤ.* d ℤ.+ (ℤ.- n) ℤ.* d          ≡˘⟨ cong (λ n+d → n ℤ.* d ℤ.+ n+d) (ℤ.neg-distribˡ-* n d) ⟩
+  n ℤ.* d ℤ.+ (ℤ.- n) ℤ.* d          ≡⟨ cong (λ n+d → n ℤ.* d ℤ.+ n+d) (ℤ.neg-distribˡ-* n d) ⟨
   n ℤ.* d ℤ.+ ℤ.- (n ℤ.* d)          ≡⟨ ℤ.+-inverseʳ (n ℤ.* d) ⟩
   0ℤ                                 ∎ where open ≡-Reasoning
 
@@ -776,9 +777,9 @@ neg⇒nonZero (mkℚᵘ (-[1+ _ ]) _) = _
 
 +-cancelˡ : ∀ {r p q} → r + p ≃ r + q → p ≃ q
 +-cancelˡ {r} {p} {q} r+p≃r+q = begin-equality
-  p            ≃˘⟨ +-identityʳ p ⟩
-  p + 0ℚᵘ      ≃˘⟨ +-congʳ p (+-inverseʳ r) ⟩
-  p + (r - r)  ≃˘⟨ +-assoc p r (- r) ⟩
+  p            ≃⟨ +-identityʳ p ⟨
+  p + 0ℚᵘ      ≃⟨ +-congʳ p (+-inverseʳ r) ⟨
+  p + (r - r)  ≃⟨ +-assoc p r (- r) ⟨
   (p + r) - r  ≃⟨ +-congˡ (- r) (+-comm p r) ⟩
   (r + p) - r  ≃⟨ +-congˡ (- r) r+p≃r+q ⟩
   (r + q) - r  ≃⟨ +-congˡ (- r) (+-comm r q) ⟩
@@ -915,26 +916,26 @@ p≃q⇒p-q≃0 p q p≃q = begin-equality
 
 p-q≃0⇒p≃q : ∀ p q → p - q ≃ 0ℚᵘ → p ≃ q
 p-q≃0⇒p≃q p q p-q≃0 = begin-equality
-  p             ≡˘⟨ +-identityʳ-≡ p ⟩
+  p             ≡⟨ +-identityʳ-≡ p ⟨
   p + 0ℚᵘ       ≃⟨ +-congʳ p (≃-sym (+-inverseˡ q)) ⟩
-  p + (- q + q) ≡˘⟨ +-assoc-≡ p (- q) q ⟩
+  p + (- q + q) ≡⟨ +-assoc-≡ p (- q) q ⟨
   (p - q) + q   ≃⟨ +-congˡ q p-q≃0 ⟩
   0ℚᵘ + q       ≡⟨ +-identityˡ-≡ q ⟩
   q             ∎ where open ≤-Reasoning
 
 neg-mono-≤ : -_ Preserves _≤_ ⟶ _≥_
 neg-mono-≤ {p@record{}} {q@record{}} (*≤* p≤q) = *≤* $ begin
-  ℤ.- ↥ q ℤ.* ↧ p   ≡˘⟨ ℤ.neg-distribˡ-* (↥ q) (↧ p) ⟩
+  ℤ.- ↥ q ℤ.* ↧ p   ≡⟨ ℤ.neg-distribˡ-* (↥ q) (↧ p) ⟨
   ℤ.- (↥ q ℤ.* ↧ p) ≤⟨ ℤ.neg-mono-≤ p≤q ⟩
   ℤ.- (↥ p ℤ.* ↧ q) ≡⟨ ℤ.neg-distribˡ-* (↥ p) (↧ q) ⟩
   ℤ.- ↥ p ℤ.* ↧ q   ∎ where open ℤ.≤-Reasoning
 
 neg-cancel-≤ : ∀ {p q} → - p ≤ - q → q ≤ p
 neg-cancel-≤ {p@record{}} {q@record{}} (*≤* -↥p↧q≤-↥q↧p) = *≤* $ begin
-  ↥ q ℤ.* ↧ p             ≡˘⟨ ℤ.neg-involutive (↥ q ℤ.* ↧ p) ⟩
+  ↥ q ℤ.* ↧ p             ≡⟨ ℤ.neg-involutive (↥ q ℤ.* ↧ p) ⟨
   ℤ.- ℤ.- (↥ q ℤ.* ↧ p)   ≡⟨ cong ℤ.-_ (ℤ.neg-distribˡ-* (↥ q) (↧ p)) ⟩
   ℤ.- ((ℤ.- ↥ q) ℤ.* ↧ p) ≤⟨ ℤ.neg-mono-≤ -↥p↧q≤-↥q↧p ⟩
-  ℤ.- ((ℤ.- ↥ p) ℤ.* ↧ q) ≡˘⟨ cong ℤ.-_ (ℤ.neg-distribˡ-* (↥ p) (↧ q)) ⟩
+  ℤ.- ((ℤ.- ↥ p) ℤ.* ↧ q) ≡⟨ cong ℤ.-_ (ℤ.neg-distribˡ-* (↥ p) (↧ q)) ⟨
   ℤ.- ℤ.- (↥ p ℤ.* ↧ q)   ≡⟨ ℤ.neg-involutive (↥ p ℤ.* ↧ q) ⟩
   ↥ p ℤ.* ↧ q             ∎
   where
@@ -948,9 +949,9 @@ p≤q⇒p-q≤0 {p} {q} p≤q = begin
 
 p-q≤0⇒p≤q : ∀ {p q} → p - q ≤ 0ℚᵘ → p ≤ q
 p-q≤0⇒p≤q {p} {q} p-q≤0 = begin
-  p             ≡˘⟨ +-identityʳ-≡ p ⟩
+  p             ≡⟨ +-identityʳ-≡ p ⟨
   p + 0ℚᵘ       ≃⟨ +-congʳ p (≃-sym (+-inverseˡ q)) ⟩
-  p + (- q + q) ≡˘⟨ +-assoc-≡ p (- q) q ⟩
+  p + (- q + q) ≡⟨ +-assoc-≡ p (- q) q ⟨
   (p - q) + q   ≤⟨ +-monoˡ-≤ q p-q≤0 ⟩
   0ℚᵘ + q       ≡⟨ +-identityˡ-≡ q ⟩
   q             ∎ where open ≤-Reasoning
@@ -963,7 +964,7 @@ p≤q⇒0≤q-p {p} {q} p≤q = begin
 
 0≤q-p⇒p≤q : ∀ {p q} → 0ℚᵘ ≤ q - p → p ≤ q
 0≤q-p⇒p≤q {p} {q} 0≤p-q = begin
-  p             ≡˘⟨ +-identityˡ-≡ p ⟩
+  p             ≡⟨ +-identityˡ-≡ p ⟨
   0ℚᵘ + p       ≤⟨ +-monoˡ-≤ p 0≤p-q ⟩
   q - p + p     ≡⟨ +-assoc-≡ q (- p) p ⟩
   q + (- p + p) ≃⟨ +-congʳ q (+-inverseˡ p) ⟩
@@ -1125,7 +1126,7 @@ p≤q⇒0≤q-p {p} {q} p≤q = begin
   (n ℕ.+ d ℕ.* suc n)       ≡⟨ cong (n ℕ.+_) (ℕ.*-suc d n) ⟩
   (n ℕ.+ (d ℕ.+ d ℕ.* n))   ≡⟨ solve 2 (λ n d → n :+ (d :+ d :* n) := d :+ (n :+ n :* d)) refl n d ⟩
   (d ℕ.+ (n ℕ.+ n ℕ.* d))   ≡⟨ cong (d ℕ.+_) (sym (ℕ.*-suc n d)) ⟩
-  d ℕ.+ n ℕ.* suc d         ≡˘⟨ ℕ.+-identityʳ _ ⟩
+  d ℕ.+ n ℕ.* suc d         ≡⟨ ℕ.+-identityʳ _ ⟨
   d ℕ.+ n ℕ.* suc d ℕ.+ 0   ∎
   where open ≡-Reasoning; open ℕ-solver
 
@@ -1149,8 +1150,8 @@ p≤q⇒0≤q-p {p} {q} p≤q = begin
 
 invertible⇒≄ : Invertible _≃_ 1ℚᵘ _*_ (p - q) → p ≄ q
 invertible⇒≄ {p} {q} (1/p-q , 1/x*x≃1 , x*1/x≃1) p≃q = 0≄1 (begin
-  0ℚᵘ             ≈˘⟨ *-zeroˡ 1/p-q ⟩
-  0ℚᵘ * 1/p-q     ≈˘⟨ *-congʳ (p≃q⇒p-q≃0 p q p≃q) ⟩
+  0ℚᵘ             ≈⟨ *-zeroˡ 1/p-q ⟨
+  0ℚᵘ * 1/p-q     ≈⟨ *-congʳ (p≃q⇒p-q≃0 p q p≃q) ⟨
   (p - q) * 1/p-q ≈⟨ x*1/x≃1 ⟩
   1ℚᵘ             ∎)
   where open ≃-Reasoning
@@ -1194,9 +1195,9 @@ neg-distribʳ-* p@record{} q@record{} =
   (↥ ((ℤ.+ p ℤ.* q) / (p ℕ.* r))) ℤ.* (↧ (q / r)) ≡⟨  cong (ℤ._* ↧ (q / r)) (↥[n/d]≡n (ℤ.+ p ℤ.* q) (p ℕ.* r)) ⟩
   (ℤ.+ p ℤ.* q) ℤ.* (↧ (q / r))                   ≡⟨  cong ((ℤ.+ p ℤ.* q) ℤ.*_) (↧[n/d]≡d q r) ⟩
   (ℤ.+ p ℤ.* q) ℤ.* ℤ.+ r                         ≡⟨  xy∙z≈y∙xz (ℤ.+ p) q (ℤ.+ r) ⟩
-  (q ℤ.* (ℤ.+ p ℤ.* ℤ.+ r))                       ≡˘⟨ cong (ℤ._* (ℤ.+ p ℤ.* ℤ.+ r)) (↥[n/d]≡n q r) ⟩
-  (↥ (q / r)) ℤ.* (ℤ.+ p ℤ.* ℤ.+ r)               ≡˘⟨  cong (↥ (q / r) ℤ.*_) (ℤ.pos-* p r) ⟩
-  (↥ (q / r)) ℤ.* (ℤ.+ (p ℕ.* r))                 ≡˘⟨ cong (↥ (q / r) ℤ.*_) (↧[n/d]≡d (ℤ.+ p ℤ.* q) (p ℕ.* r)) ⟩
+  (q ℤ.* (ℤ.+ p ℤ.* ℤ.+ r))                       ≡⟨ cong (ℤ._* (ℤ.+ p ℤ.* ℤ.+ r)) (↥[n/d]≡n q r) ⟨
+  (↥ (q / r)) ℤ.* (ℤ.+ p ℤ.* ℤ.+ r)               ≡⟨  cong (↥ (q / r) ℤ.*_) (ℤ.pos-* p r) ⟨
+  (↥ (q / r)) ℤ.* (ℤ.+ (p ℕ.* r))                 ≡⟨ cong (↥ (q / r) ℤ.*_) (↧[n/d]≡d (ℤ.+ p ℤ.* q) (p ℕ.* r)) ⟨
   (↥ (q / r)) ℤ.* (↧ ((ℤ.+ p ℤ.* q) / (p ℕ.* r))) ∎)
   where open ℤ.≤-Reasoning
 
@@ -1233,11 +1234,11 @@ private
 
 *-cancelʳ-≤-neg : ∀ r .{{_ : Negative r}} → p * r ≤ q * r → q ≤ p
 *-cancelʳ-≤-neg {p} {q} r@(mkℚᵘ -[1+ _ ] _) pr≤qr = neg-cancel-≤ (*-cancelʳ-≤-pos (- r) (begin
-  - p * - r    ≃˘⟨ neg-distribˡ-* p (- r) ⟩
-  - (p * - r)  ≃˘⟨ -‿cong (neg-distribʳ-* p r) ⟩
+  - p * - r    ≃⟨ neg-distribˡ-* p (- r) ⟨
+  - (p * - r)  ≃⟨ -‿cong (neg-distribʳ-* p r) ⟨
   - - (p * r)  ≃⟨ neg-involutive (p * r) ⟩
   p * r        ≤⟨ pr≤qr ⟩
-  q * r        ≃˘⟨ neg-involutive (q * r) ⟩
+  q * r        ≃⟨ neg-involutive (q * r) ⟨
   - - (q * r)  ≃⟨ -‿cong (neg-distribʳ-* q r) ⟩
   - (q * - r)  ≃⟨ neg-distribˡ-* q (- r) ⟩
   - q * - r    ∎))
@@ -1249,7 +1250,7 @@ private
 *-monoˡ-≤-nonNeg : ∀ r .{{_ : NonNegative r}} → (_* r) Preserves _≤_ ⟶ _≤_
 *-monoˡ-≤-nonNeg r@(mkℚᵘ (ℤ.+ n) _) {p@record{}} {q@record{}} (*≤* x<y) = *≤* $ begin
   ↥ p ℤ.* ↥ r ℤ.* (↧ q   ℤ.* ↧ r)  ≡⟨  reorder₂ (↥ p) _ _ _ ⟩
-  l₁          ℤ.* (ℤ.+ n ℤ.* ↧ r)  ≡˘⟨  cong (l₁ ℤ.*_) (ℤ.pos-* n _) ⟩
+  l₁          ℤ.* (ℤ.+ n ℤ.* ↧ r)  ≡⟨  cong (l₁ ℤ.*_) (ℤ.pos-* n _) ⟨
   l₁          ℤ.* ℤ.+ (n ℕ.* ↧ₙ r) ≤⟨  ℤ.*-monoʳ-≤-nonNeg (ℤ.+ (n ℕ.* ↧ₙ r)) x<y ⟩
   l₂          ℤ.* ℤ.+ (n ℕ.* ↧ₙ r) ≡⟨ cong (l₂ ℤ.*_) (ℤ.pos-* n _) ⟩
   l₂          ℤ.* (ℤ.+ n ℤ.* ↧ r)  ≡⟨  reorder₂ (↥ q) _ _ _ ⟩
@@ -1269,10 +1270,10 @@ private
 
 *-monoˡ-≤-nonPos : ∀ r .{{_ : NonPositive r}} → (_* r) Preserves _≤_ ⟶ _≥_
 *-monoˡ-≤-nonPos r {p} {q} p≤q = begin
-  q * r        ≃˘⟨ neg-involutive (q * r) ⟩
+  q * r        ≃⟨ neg-involutive (q * r) ⟨
   - - (q * r)  ≃⟨  -‿cong (neg-distribʳ-* q r) ⟩
   - (q * - r)  ≤⟨  neg-mono-≤ (*-monoˡ-≤-nonNeg (- r) {{ -r≥0}} p≤q) ⟩
-  - (p * - r)  ≃˘⟨ -‿cong (neg-distribʳ-* p r) ⟩
+  - (p * - r)  ≃⟨ -‿cong (neg-distribʳ-* p r) ⟨
   - - (p * r)  ≃⟨  neg-involutive (p * r) ⟩
   p * r        ∎
   where open ≤-Reasoning; -r≥0 = nonNegative (neg-mono-≤ (nonPositive⁻¹ r))
@@ -1287,7 +1288,7 @@ private
 *-monoˡ-<-pos r@record{} {p@record{}} {q@record{}} (*<* x<y) = *<* $ begin-strict
   ↥ p ℤ.*  ↥ r ℤ.* (↧ q  ℤ.* ↧ r) ≡⟨ reorder₁ (↥ p) _ _ _ ⟩
   ↥ p ℤ.*  ↧ q ℤ.*  ↥ r  ℤ.* ↧ r  <⟨ ℤ.*-monoʳ-<-pos (↧ r) (ℤ.*-monoʳ-<-pos (↥ r) x<y) ⟩
-  ↥ q ℤ.*  ↧ p ℤ.*  ↥ r  ℤ.* ↧ r  ≡˘⟨ reorder₁ (↥ q) _ _ _ ⟩
+  ↥ q ℤ.*  ↧ p ℤ.*  ↥ r  ℤ.* ↧ r  ≡⟨ reorder₁ (↥ q) _ _ _ ⟨
   ↥ q ℤ.*  ↥ r ℤ.* (↧ p  ℤ.* ↧ r) ∎ where open ℤ.≤-Reasoning
 
 *-monoʳ-<-pos : ∀ r .{{_ : Positive r}} → (r *_) Preserves _<_ ⟶ _<_
@@ -1314,10 +1315,10 @@ private
 
 *-monoˡ-<-neg : ∀ r .{{_ :  Negative r}} → (_* r) Preserves _<_ ⟶ _>_
 *-monoˡ-<-neg r {p} {q} p<q = begin-strict
-  q * r        ≃˘⟨ neg-involutive (q * r) ⟩
+  q * r        ≃⟨ neg-involutive (q * r) ⟨
   - - (q * r)  ≃⟨ -‿cong (neg-distribʳ-* q r) ⟩
   - (q * - r)  <⟨ neg-mono-< (*-monoˡ-<-pos (- r) {{ -r>0}} p<q) ⟩
-  - (p * - r)  ≃˘⟨ -‿cong (neg-distribʳ-* p r) ⟩
+  - (p * - r)  ≃⟨ -‿cong (neg-distribʳ-* p r) ⟨
   - - (p * r)  ≃⟨ neg-involutive (p * r) ⟩
   p * r        ∎
   where open ≤-Reasoning; -r>0 = positive (neg-mono-< (negative⁻¹ r))
@@ -1328,7 +1329,7 @@ private
 *-cancelˡ-<-nonPos : ∀ r .{{_ : NonPositive r}} → r * p < r * q → q < p
 *-cancelˡ-<-nonPos {p} {q} r rp<rq =
   *-cancelˡ-<-nonNeg (- r) {{ -r≥0}} $ begin-strict
-    - r * q    ≃˘⟨ neg-distribˡ-* r q ⟩
+    - r * q    ≃⟨ neg-distribˡ-* r q ⟨
     - (r * q)  <⟨ neg-mono-< rp<rq ⟩
     - (r * p)  ≃⟨ neg-distribˡ-* r p ⟩
     - r * p    ∎
@@ -1495,8 +1496,8 @@ p>1⇒1/p<1 {p} p>1 = lemma′ p (p>1⇒p≢0 p>1) p>1
 1/-antimono-≤-pos : ∀ {p q} .{{_ : Positive p}} .{{_ : Positive q}} →
                     p ≤ q → (1/ q) {{pos⇒nonZero q}} ≤ (1/ p) {{pos⇒nonZero p}}
 1/-antimono-≤-pos {p} {q} p≤q = begin
-  1/q              ≃˘⟨ *-identityˡ 1/q ⟩
-  1ℚᵘ * 1/q        ≃˘⟨ *-congʳ (*-inverseˡ p) ⟩
+  1/q              ≃⟨ *-identityˡ 1/q ⟨
+  1ℚᵘ * 1/q        ≃⟨ *-congʳ (*-inverseˡ p) ⟨
   (1/p * p) * 1/q  ≤⟨  *-monoˡ-≤-nonNeg 1/q (*-monoʳ-≤-nonNeg 1/p p≤q) ⟩
   (1/p * q) * 1/q  ≃⟨  *-assoc 1/p q 1/q ⟩
   1/p * (q * 1/q)  ≃⟨  *-congˡ {1/p} (*-inverseʳ q) ⟩
@@ -1775,7 +1776,7 @@ pos⊔pos⇒pos p q = positive (⊔-mono-< (positive⁻¹ p) (positive⁻¹ q))
   ℤ.- ℤ.- (↥ ∣ p ∣ ℤ.* ↧ q)  ≡⟨ cong ℤ.-_ (ℤ.neg-distribˡ-* (↥ ∣ p ∣) (↧ q)) ⟩
   ℤ.- (↥ p ℤ.* ↧ q)          ≡⟨ cong ℤ.-_ ↥p↧q≡↥q↧p ⟩
   ℤ.- (↥ q ℤ.* ↧ p)          ≡⟨ cong ℤ.-_ (ℤ.neg-distribˡ-* (↥ ∣ q ∣) (↧ p)) ⟩
-  ℤ.- ℤ.- (↥ ∣ q ∣ ℤ.* ↧ p)  ≡˘⟨ ℤ.neg-involutive _ ⟩
+  ℤ.- ℤ.- (↥ ∣ q ∣ ℤ.* ↧ p)  ≡⟨ ℤ.neg-involutive _ ⟨
   ↥ ∣ q ∣ ℤ.* ↧ p            ∎)
   where open ≡-Reasoning
 
@@ -1807,7 +1808,7 @@ pos⊔pos⇒pos p q = positive (⊔-mono-< (positive⁻¹ p) (positive⁻¹ q))
 ∣p∣≡p⇒0≤p {mkℚᵘ (ℤ.+ n) d-1} ∣p∣≡p = *≤* (begin
   0ℤ ℤ.* +[1+ d-1 ]  ≡⟨ ℤ.*-zeroˡ (ℤ.+ d-1) ⟩
   0ℤ                 ≤⟨ ℤ.+≤+ ℕ.z≤n ⟩
-  ℤ.+ n              ≡˘⟨ ℤ.*-identityʳ (ℤ.+ n) ⟩
+  ℤ.+ n              ≡⟨ ℤ.*-identityʳ (ℤ.+ n) ⟨
   ℤ.+ n ℤ.* 1ℤ       ∎)
   where open ℤ.≤-Reasoning
 
@@ -1826,7 +1827,7 @@ pos⊔pos⇒pos p q = positive (⊔-mono-< (positive⁻¹ p) (positive⁻¹ q))
   ↥ ∣ (↥p↧q ℤ.+ ↥q↧p) / ↧p↧q ∣ ℤ.* ℤ.+ ↧p↧q        ≡⟨⟩
   ↥ (ℤ.+ ℤ.∣ ↥p↧q ℤ.+ ↥q↧p ∣ / ↧p↧q) ℤ.* ℤ.+ ↧p↧q  ≡⟨ cong (ℤ._* ℤ.+ ↧p↧q) (↥[n/d]≡n (ℤ.+ ℤ.∣ ↥p↧q ℤ.+ ↥q↧p ∣) ↧p↧q) ⟩
   ℤ.+ ℤ.∣ ↥p↧q ℤ.+ ↥q↧p ∣ ℤ.* ℤ.+ ↧p↧q             ≤⟨ ℤ.*-monoʳ-≤-nonNeg (ℤ.+ ↧p↧q) (ℤ.+≤+ (ℤ.∣i+j∣≤∣i∣+∣j∣ ↥p↧q ↥q↧p)) ⟩
-  (ℤ.+ ℤ.∣ ↥p↧q ∣ ℤ.+ ℤ.+ ℤ.∣ ↥q↧p ∣) ℤ.* ℤ.+ ↧p↧q ≡˘⟨ cong₂ (λ h₁ h₂ → (h₁ ℤ.+ h₂) ℤ.* ℤ.+ ↧p↧q) ∣↥p∣↧q≡∣↥p↧q∣ ∣↥q∣↧p≡∣↥q↧p∣ ⟩
+  (ℤ.+ ℤ.∣ ↥p↧q ∣ ℤ.+ ℤ.+ ℤ.∣ ↥q↧p ∣) ℤ.* ℤ.+ ↧p↧q ≡⟨ cong₂ (λ h₁ h₂ → (h₁ ℤ.+ h₂) ℤ.* ℤ.+ ↧p↧q) ∣↥p∣↧q≡∣↥p↧q∣ ∣↥q∣↧p≡∣↥q↧p∣ ⟨
   (∣↥p∣↧q ℤ.+ ∣↥q∣↧p) ℤ.* ℤ.+ ↧p↧q                 ≡⟨⟩
   (↥∣p∣↧q ℤ.+ ↥∣q∣↧p) ℤ.* ℤ.+ ↧p↧q                 ≡⟨ cong (ℤ._* ℤ.+ ↧p↧q) (↥[n/d]≡n (↥∣p∣↧q ℤ.+ ↥∣q∣↧p) ↧p↧q) ⟩
   ↥ ((↥∣p∣↧q ℤ.+ ↥∣q∣↧p) / ↧p↧q) ℤ.* ℤ.+ ↧p↧q      ≡⟨⟩
@@ -1843,9 +1844,9 @@ pos⊔pos⇒pos p q = positive (⊔-mono-< (positive⁻¹ p) (positive⁻¹ q))
     ∣m∣n≡∣mn∣ : ∀ m n → ℤ.+ ℤ.∣ m ∣ ℤ.* ℤ.+ n ≡ ℤ.+ ℤ.∣ m ℤ.* ℤ.+ n ∣
     ∣m∣n≡∣mn∣ m n = begin-equality
       ℤ.+ ℤ.∣ m ∣ ℤ.* ℤ.+ n                        ≡⟨⟩
-      ℤ.+ ℤ.∣ m ∣ ℤ.* ℤ.+ ℤ.∣ ℤ.+ n ∣              ≡˘⟨ ℤ.pos-* ℤ.∣ m ∣ ℤ.∣ ℤ.+ n ∣ ⟩
+      ℤ.+ ℤ.∣ m ∣ ℤ.* ℤ.+ ℤ.∣ ℤ.+ n ∣              ≡⟨ ℤ.pos-* ℤ.∣ m ∣ ℤ.∣ ℤ.+ n ∣ ⟨
       ℤ.+ (ℤ.∣ m ∣ ℕ.* n)                          ≡⟨⟩
-      ℤ.+ (ℤ.∣ m ∣ ℕ.* ℤ.∣ ℤ.+ n ∣)                ≡˘⟨ cong ℤ.+_ (ℤ.∣i*j∣≡∣i∣*∣j∣ m (ℤ.+ n)) ⟩
+      ℤ.+ (ℤ.∣ m ∣ ℕ.* ℤ.∣ ℤ.+ n ∣)                ≡⟨ cong ℤ.+_ (ℤ.∣i*j∣≡∣i∣*∣j∣ m (ℤ.+ n)) ⟨
       ℤ.+ (ℤ.∣ m ℤ.* ℤ.+ n ∣)                      ∎
     ∣↥p∣↧q≡∣↥p↧q∣ : ∣↥p∣↧q ≡ ℤ.+ ℤ.∣ ↥p↧q ∣
     ∣↥p∣↧q≡∣↥p↧q∣ = ∣m∣n≡∣mn∣ (↥ p) (↧ₙ q)
diff --git a/src/Data/Tree/Binary/Zipper/Properties.agda b/src/Data/Tree/Binary/Zipper/Properties.agda
index 107981bcbf..fa2f09c190 100644
--- a/src/Data/Tree/Binary/Zipper/Properties.agda
+++ b/src/Data/Tree/Binary/Zipper/Properties.agda
@@ -60,9 +60,9 @@ toTree-#nodes (mkZipper c v) = helper c v
       #ctx = sum (List.map (suc ∘ BT.#nodes ∘ getTree) ctx)
       #foc = BT.#nodes foc
       #l = BT.#nodes l in begin
-      #foc + (1 + (#l + #ctx))             ≡˘⟨ +-assoc #foc 1 (#l + #ctx) ⟩
+      #foc + (1 + (#l + #ctx))             ≡⟨ +-assoc #foc 1 (#l + #ctx) ⟨
       #foc + 1 + (#l + #ctx)               ≡⟨ cong (_+ (#l + #ctx)) (+-comm #foc 1) ⟩
-      1 + #foc + (#l + #ctx)               ≡˘⟨ +-assoc (1 + #foc) #l #ctx ⟩
+      1 + #foc + (#l + #ctx)               ≡⟨ +-assoc (1 + #foc) #l #ctx ⟨
       1 + #foc + #l + #ctx                 ≡⟨ cong (_+ #ctx) (+-comm (1 + #foc) #l) ⟩
       #nodes (mkZipper ctx (node l m foc)) ≡⟨ helper ctx (node l m foc) ⟩
       BT.#nodes (toTree (mkZipper cs foc)) ∎
@@ -70,8 +70,8 @@ toTree-#nodes (mkZipper c v) = helper c v
       #ctx = sum (List.map (suc ∘ BT.#nodes ∘ getTree) ctx)
       #foc = BT.#nodes foc
       #r = BT.#nodes r in begin
-      #foc + (1 + (#r + #ctx))             ≡˘⟨ cong (#foc +_) (+-assoc 1 #r #ctx) ⟩
-      #foc + (1 + #r + #ctx)               ≡˘⟨ +-assoc #foc (suc #r) #ctx ⟩
+      #foc + (1 + (#r + #ctx))             ≡⟨ cong (#foc +_) (+-assoc 1 #r #ctx) ⟨
+      #foc + (1 + #r + #ctx)               ≡⟨ +-assoc #foc (suc #r) #ctx ⟨
       #nodes (mkZipper ctx (node foc m r)) ≡⟨ helper ctx (node foc m r) ⟩
       BT.#nodes (toTree (mkZipper cs foc)) ∎
 
@@ -86,7 +86,7 @@ toTree-#leaves (mkZipper c v) = helper c v
       #ctx = sum (List.map (BT.#leaves ∘ getTree) ctx)
       #foc = BT.#leaves foc
       #l = BT.#leaves l in begin
-      #foc + (#l + #ctx)                    ≡˘⟨ +-assoc #foc #l #ctx ⟩
+      #foc + (#l + #ctx)                    ≡⟨ +-assoc #foc #l #ctx ⟨
       #foc + #l + #ctx                      ≡⟨ cong (_+ #ctx) (+-comm #foc #l) ⟩
       #leaves (mkZipper ctx (node l m foc)) ≡⟨ helper ctx (node l m foc) ⟩
       BT.#leaves (toTree (mkZipper cs foc)) ∎
@@ -94,7 +94,7 @@ toTree-#leaves (mkZipper c v) = helper c v
       #ctx = sum (List.map (BT.#leaves ∘ getTree) ctx)
       #foc = BT.#leaves foc
       #r = BT.#leaves r in begin
-      #foc + (#r + #ctx)                    ≡˘⟨ +-assoc #foc #r #ctx ⟩
+      #foc + (#r + #ctx)                    ≡⟨ +-assoc #foc #r #ctx ⟨
       #leaves (mkZipper ctx (node foc m r)) ≡⟨ helper ctx (node foc m r) ⟩
       BT.#leaves (toTree (mkZipper cs foc)) ∎
 
diff --git a/src/Data/Tree/Rose/Properties.agda b/src/Data/Tree/Rose/Properties.agda
index 749bdb5748..054103fdd1 100644
--- a/src/Data/Tree/Rose/Properties.agda
+++ b/src/Data/Tree/Rose/Properties.agda
@@ -39,7 +39,7 @@ map-∘ f g (node a ts) = cong (node (g (f a))) $ begin
 
 depth-map : (f : A → B) (t : Rose A i) → depth {i = i} (map {i = i} f t) ≡ depth {i = i} t
 depth-map f (node a ts) = cong (suc ∘′ max 0) $ begin
-  List.map depth (List.map (map f) ts) ≡˘⟨ Listₚ.map-∘ ts ⟩
+  List.map depth (List.map (map f) ts) ≡⟨ Listₚ.map-∘ ts ⟨
   List.map (depth ∘′ map f) ts         ≡⟨ Listₚ.map-cong (depth-map f) ts ⟩
   List.map depth ts ∎
 
@@ -49,7 +49,7 @@ depth-map f (node a ts) = cong (suc ∘′ max 0) $ begin
 foldr-map : (f : A → B) (n : B → List C → C) (ts : Rose A i) →
             foldr {i = i} n (map {i = i} f ts) ≡ foldr {i = i} (n ∘′ f) ts
 foldr-map f n (node a ts) = cong (n (f a)) $ begin
-  List.map (foldr n) (List.map (map f) ts) ≡˘⟨ Listₚ.map-∘ ts ⟩
+  List.map (foldr n) (List.map (map f) ts) ≡⟨ Listₚ.map-∘ ts ⟨
   List.map (foldr n ∘′ map f) ts           ≡⟨ Listₚ.map-cong (foldr-map f n) ts ⟩
   List.map (foldr (n ∘′ f)) ts             ∎
 
diff --git a/src/Data/Vec/Functional/Properties.agda b/src/Data/Vec/Functional/Properties.agda
index 93f95b423b..d1d5f8c628 100644
--- a/src/Data/Vec/Functional/Properties.agda
+++ b/src/Data/Vec/Functional/Properties.agda
@@ -181,20 +181,20 @@ module _ {ys ys′ : Vector A m} where
   ... | yes i<n = begin
     (xs ++ ys) i      ≡⟨ lookup-++-< xs ys i i<n ⟩
     xs (fromℕ< i<n)   ≡⟨ eq₁ (fromℕ< i<n) ⟩
-    xs′ (fromℕ< i<n)  ≡˘⟨ lookup-++-< xs′ ys′ i i<n ⟩
+    xs′ (fromℕ< i<n)  ≡⟨ lookup-++-< xs′ ys′ i i<n ⟨
     (xs′ ++ ys′) i    ∎
     where open ≡-Reasoning
   ... | no i≮n = begin
     (xs ++ ys) i               ≡⟨ lookup-++-≥ xs ys i (ℕₚ.≮⇒≥ i≮n) ⟩
     ys (reduce≥ i (ℕₚ.≮⇒≥ i≮n))   ≡⟨ eq₂ (reduce≥ i (ℕₚ.≮⇒≥ i≮n)) ⟩
-    ys′ (reduce≥ i (ℕₚ.≮⇒≥ i≮n))  ≡˘⟨ lookup-++-≥ xs′ ys′ i (ℕₚ.≮⇒≥ i≮n) ⟩
+    ys′ (reduce≥ i (ℕₚ.≮⇒≥ i≮n))  ≡⟨ lookup-++-≥ xs′ ys′ i (ℕₚ.≮⇒≥ i≮n) ⟨
     (xs′ ++ ys′) i             ∎
     where open ≡-Reasoning
 
   ++-injectiveˡ : ∀ (xs xs′ : Vector A n) →
                   xs ++ ys ≗ xs′ ++ ys′ → xs ≗ xs′
   ++-injectiveˡ xs xs′ eq i = begin
-    xs i                   ≡˘⟨ lookup-++ˡ xs ys i ⟩
+    xs i                   ≡⟨ lookup-++ˡ xs ys i ⟨
     (xs ++ ys) (i ↑ˡ m)    ≡⟨ eq (i ↑ˡ m) ⟩
     (xs′ ++ ys′) (i ↑ˡ m)  ≡⟨ lookup-++ˡ xs′ ys′ i ⟩
     xs′ i                  ∎
@@ -202,7 +202,7 @@ module _ {ys ys′ : Vector A m} where
 
   ++-injectiveʳ : ∀ (xs xs′ : Vector A n) → xs ++ ys ≗ xs′ ++ ys′ → ys ≗ ys′
   ++-injectiveʳ {n} xs xs′ eq i = begin
-    ys i                   ≡˘⟨ lookup-++ʳ xs ys i ⟩
+    ys i                   ≡⟨ lookup-++ʳ xs ys i ⟨
     (xs ++ ys) (n ↑ʳ i)    ≡⟨ eq (n ↑ʳ i)   ⟩
     (xs′ ++ ys′) (n ↑ʳ i)  ≡⟨ lookup-++ʳ xs′ ys′ i ⟩
     ys′ i                  ∎
diff --git a/src/Data/Vec/Properties.agda b/src/Data/Vec/Properties.agda
index 38793a9038..4c5801fd7b 100644
--- a/src/Data/Vec/Properties.agda
+++ b/src/Data/Vec/Properties.agda
@@ -955,13 +955,13 @@ foldr-reverse B f {e} xs = foldl-fusion (foldr B f e) refl (λ _ _ → refl) xs
 reverse-involutive : Involutive {A = Vec A n} _≡_ reverse
 reverse-involutive xs = begin
   reverse (reverse xs)    ≡⟨  foldl-reverse (Vec _) (flip _∷_) xs ⟩
-  foldr (Vec _) _∷_ [] xs ≡˘⟨ id-is-foldr xs ⟩
+  foldr (Vec _) _∷_ [] xs ≡⟨ id-is-foldr xs ⟨
   xs                      ∎
   where open ≡-Reasoning
 
 reverse-reverse : reverse xs ≡ ys → reverse ys ≡ xs
 reverse-reverse {xs = xs} {ys} eq =  begin
-  reverse ys           ≡˘⟨ cong reverse eq ⟩
+  reverse ys           ≡⟨ cong reverse eq ⟨
   reverse (reverse xs) ≡⟨  reverse-involutive xs ⟩
   xs                   ∎
   where open ≡-Reasoning
@@ -970,7 +970,7 @@ reverse-reverse {xs = xs} {ys} eq =  begin
 
 reverse-injective : reverse xs ≡ reverse ys → xs ≡ ys
 reverse-injective {xs = xs} {ys} eq = begin
-  xs                   ≡˘⟨ reverse-reverse eq ⟩
+  xs                   ≡⟨ reverse-reverse eq ⟨
   reverse (reverse ys) ≡⟨  reverse-involutive ys ⟩
   ys                   ∎
   where open ≡-Reasoning
@@ -1000,7 +1000,7 @@ map-reverse f (x ∷ xs) = begin
   map f (reverse (x ∷ xs))  ≡⟨  cong (map f) (reverse-∷ x xs) ⟩
   map f (reverse xs ∷ʳ x)   ≡⟨  map-∷ʳ f x (reverse xs) ⟩
   map f (reverse xs) ∷ʳ f x ≡⟨  cong (_∷ʳ f x) (map-reverse f xs ) ⟩
-  reverse (map f xs) ∷ʳ f x ≡˘⟨ reverse-∷ (f x) (map f xs) ⟩
+  reverse (map f xs) ∷ʳ f x ≡⟨ reverse-∷ (f x) (map f xs) ⟨
   reverse (f x ∷ map f xs)  ≡⟨⟩
   reverse (map f (x ∷ xs))  ∎
   where open ≡-Reasoning
@@ -1015,7 +1015,7 @@ reverse-++ {m = suc m} {n = n} eq (x ∷ xs) ys = begin
   reverse (xs ++ ys) ∷ʳ x             ≈⟨ ≈-cong (_∷ʳ x) (cast-∷ʳ (cong suc (+-comm m n)) x (reverse (xs ++ ys)))
                                                 (reverse-++ _ xs ys) ⟩
   (reverse ys ++ reverse xs) ∷ʳ x     ≈⟨ ++-∷ʳ (sym (+-suc n m)) x (reverse ys) (reverse xs) ⟩
-  reverse ys ++ (reverse xs ∷ʳ x)     ≂˘⟨ cong (reverse ys ++_) (reverse-∷ x xs) ⟩
+  reverse ys ++ (reverse xs ∷ʳ x)     ≂⟨ cong (reverse ys ++_) (reverse-∷ x xs) ⟨
   reverse ys ++ (reverse (x ∷ xs))    ∎
   where open CastReasoning
 
@@ -1025,7 +1025,7 @@ cast-reverse {n = suc n} eq (x ∷ xs) = begin
   reverse (x ∷ xs)           ≂⟨ reverse-∷ x xs ⟩
   reverse xs ∷ʳ x            ≈⟨ ≈-cong (_∷ʳ x) (cast-∷ʳ eq x (reverse xs))
                                        (cast-reverse (cong pred eq) xs) ⟩
-  reverse (cast _ xs) ∷ʳ x   ≂˘⟨ reverse-∷ x (cast (cong pred eq) xs) ⟩
+  reverse (cast _ xs) ∷ʳ x   ≂⟨ reverse-∷ x (cast (cong pred eq) xs) ⟨
   reverse (x ∷ cast _ xs)    ≈⟨⟩
   reverse (cast eq (x ∷ xs)) ∎
   where open CastReasoning
@@ -1054,7 +1054,7 @@ map-ʳ++ {ys = ys} f xs = begin
   map f (xs ʳ++ ys)              ≡⟨  cong (map f) (unfold-ʳ++ xs ys) ⟩
   map f (reverse xs ++ ys)       ≡⟨  map-++ f (reverse xs) ys ⟩
   map f (reverse xs) ++ map f ys ≡⟨  cong (_++ map f ys) (map-reverse f xs) ⟩
-  reverse (map f xs) ++ map f ys ≡˘⟨ unfold-ʳ++ (map f xs) (map f ys) ⟩
+  reverse (map f xs) ++ map f ys ≡⟨ unfold-ʳ++ (map f xs) (map f ys) ⟨
   map f xs ʳ++ map f ys          ∎
   where open ≡-Reasoning
 
@@ -1064,7 +1064,7 @@ map-ʳ++ {ys = ys} f xs = begin
   (a ∷ xs) ʳ++ ys         ≂⟨ unfold-ʳ++ (a ∷ xs) ys ⟩
   reverse (a ∷ xs) ++ ys  ≂⟨ cong (_++ ys) (reverse-∷ a xs) ⟩
   (reverse xs ∷ʳ a) ++ ys ≈⟨ ∷ʳ-++ eq a (reverse xs) ⟩
-  reverse xs ++ (a ∷ ys)  ≂˘⟨ unfold-ʳ++ xs (a ∷ ys) ⟩
+  reverse xs ++ (a ∷ ys)  ≂⟨ unfold-ʳ++ xs (a ∷ ys) ⟨
   xs ʳ++ (a ∷ ys)         ∎
   where open CastReasoning
 
@@ -1075,8 +1075,8 @@ map-ʳ++ {ys = ys} f xs = begin
   reverse (xs ++ ys) ++ zs         ≈⟨ ≈-cong (_++ zs) (cast-++ˡ (+-comm m n) (reverse (xs ++ ys)))
                                              (reverse-++ (+-comm m n) xs ys) ⟩
   (reverse ys ++ reverse xs) ++ zs ≈⟨ ++-assoc (trans (cong (_+ o) (+-comm n m)) eq) (reverse ys) (reverse xs) zs ⟩
-  reverse ys ++ (reverse xs ++ zs) ≂˘⟨ cong (reverse ys ++_) (unfold-ʳ++ xs zs) ⟩
-  reverse ys ++ (xs ʳ++ zs)        ≂˘⟨ unfold-ʳ++ ys (xs ʳ++ zs) ⟩
+  reverse ys ++ (reverse xs ++ zs) ≂⟨ cong (reverse ys ++_) (unfold-ʳ++ xs zs) ⟨
+  reverse ys ++ (xs ʳ++ zs)        ≂⟨ unfold-ʳ++ ys (xs ʳ++ zs) ⟨
   ys ʳ++ (xs ʳ++ zs)               ∎
   where open CastReasoning
 
@@ -1089,7 +1089,7 @@ map-ʳ++ {ys = ys} f xs = begin
                                                        (reverse-++ (+-comm m n) (reverse xs) ys) ⟩
   (reverse ys ++ reverse (reverse xs)) ++ zs ≂⟨ cong ((_++ zs) ∘ (reverse ys ++_)) (reverse-involutive xs) ⟩
   (reverse ys ++ xs) ++ zs                   ≈⟨ ++-assoc (+-assoc n m o) (reverse ys) xs zs ⟩
-  reverse ys ++ (xs ++ zs)                   ≂˘⟨ unfold-ʳ++ ys (xs ++ zs) ⟩
+  reverse ys ++ (xs ++ zs)                   ≂⟨ unfold-ʳ++ ys (xs ++ zs) ⟨
   ys ʳ++ (xs ++ zs)                          ∎
   where open CastReasoning
 
@@ -1100,7 +1100,7 @@ sum-++ : ∀ (xs : Vec ℕ m) → sum (xs ++ ys) ≡ sum xs + sum ys
 sum-++ {_}       []       = refl
 sum-++ {ys = ys} (x ∷ xs) = begin
   x + sum (xs ++ ys)     ≡⟨  cong (x +_) (sum-++ xs) ⟩
-  x + (sum xs + sum ys)  ≡˘⟨ +-assoc x (sum xs) (sum ys) ⟩
+  x + (sum xs + sum ys)  ≡⟨ +-assoc x (sum xs) (sum ys) ⟨
   sum (x ∷ xs) + sum ys  ∎
   where open ≡-Reasoning
 
@@ -1209,7 +1209,7 @@ tabulate-allFin f = tabulate-∘ f id
 
 map-lookup-allFin : ∀ (xs : Vec A n) → map (lookup xs) (allFin n) ≡ xs
 map-lookup-allFin {n = n} xs = begin
-  map (lookup xs) (allFin n) ≡˘⟨ tabulate-∘ (lookup xs) id ⟩
+  map (lookup xs) (allFin n) ≡⟨ tabulate-∘ (lookup xs) id ⟨
   tabulate (lookup xs)       ≡⟨ tabulate∘lookup xs ⟩
   xs                         ∎
   where open ≡-Reasoning
@@ -1315,10 +1315,10 @@ fromList-reverse List.[] = refl
 fromList-reverse (x List.∷ xs) = begin
   fromList (List.reverse (x List.∷ xs))         ≈⟨ cast-fromList (Listₚ.ʳ++-defn xs) ⟩
   fromList (List.reverse xs List.++ List.[ x ]) ≈⟨ fromList-++ (List.reverse xs) ⟩
-  fromList (List.reverse xs) ++ [ x ]           ≈˘⟨ unfold-∷ʳ (+-comm 1 _) x (fromList (List.reverse xs)) ⟩
+  fromList (List.reverse xs) ++ [ x ]           ≈⟨ unfold-∷ʳ (+-comm 1 _) x (fromList (List.reverse xs)) ⟨
   fromList (List.reverse xs) ∷ʳ x               ≈⟨ ≈-cong (_∷ʳ x) (cast-∷ʳ (cong suc (Listₚ.length-reverse xs)) _ _)
                                                           (fromList-reverse xs) ⟩
-  reverse (fromList xs) ∷ʳ x                    ≂˘⟨ reverse-∷ x (fromList xs) ⟩
+  reverse (fromList xs) ∷ʳ x                    ≂⟨ reverse-∷ x (fromList xs) ⟨
   reverse (x ∷ fromList xs)                     ≈⟨⟩
   reverse (fromList (x List.∷ xs))              ∎
   where open CastReasoning
diff --git a/src/Data/Vec/Relation/Binary/Equality/Cast.agda b/src/Data/Vec/Relation/Binary/Equality/Cast.agda
index f65981f7a3..cc18556ea7 100644
--- a/src/Data/Vec/Relation/Binary/Equality/Cast.agda
+++ b/src/Data/Vec/Relation/Binary/Equality/Cast.agda
@@ -52,7 +52,7 @@ xs ≈[ eq ] ys = cast eq xs ≡ ys
 
 ≈-sym : .{m≡n : m ≡ n} → Sym _≈[ m≡n ]_ _≈[ sym m≡n ]_
 ≈-sym {m≡n = m≡n} {xs} {ys} xs≈ys = begin
-  cast (sym m≡n) ys             ≡˘⟨ cong (cast (sym m≡n)) xs≈ys ⟩
+  cast (sym m≡n) ys             ≡⟨ cong (cast (sym m≡n)) xs≈ys ⟨
   cast (sym m≡n) (cast m≡n xs)  ≡⟨ cast-trans m≡n (sym m≡n) xs ⟩
   cast (trans m≡n (sym m≡n)) xs ≡⟨ cast-is-id (trans m≡n (sym m≡n)) xs ⟩
   xs                            ∎
@@ -60,7 +60,7 @@ xs ≈[ eq ] ys = cast eq xs ≡ ys
 
 ≈-trans : ∀ .{m≡n : m ≡ n} .{n≡o : n ≡ o} → Trans _≈[ m≡n ]_ _≈[ n≡o ]_ _≈[ trans m≡n n≡o ]_
 ≈-trans {m≡n = m≡n} {n≡o} {xs} {ys} {zs} xs≈ys ys≈zs = begin
-  cast (trans m≡n n≡o) xs ≡˘⟨ cast-trans m≡n n≡o xs ⟩
+  cast (trans m≡n n≡o) xs ≡⟨ cast-trans m≡n n≡o xs ⟨
   cast n≡o (cast m≡n xs)  ≡⟨ cong (cast n≡o) xs≈ys ⟩
   cast n≡o ys             ≡⟨ ys≈zs ⟩
   zs                      ∎
@@ -84,18 +84,28 @@ module CastReasoning where
   xs ≈⟨⟩ xs≈ys = xs≈ys
 
   -- composition of _≈[_]_
-  step-≈ : ∀ .{m≡n : m ≡ n}.{m≡o : m ≡ o} (xs : Vec A m) {ys : Vec A n} {zs : Vec A o} →
+  step-≈-⟩ : ∀ .{m≡n : m ≡ n}.{m≡o : m ≡ o} (xs : Vec A m) {ys : Vec A n} {zs : Vec A o} →
            ys ≈[ trans (sym m≡n) m≡o ] zs → xs ≈[ m≡n ] ys → xs ≈[ m≡o ] zs
-  step-≈ xs ys≈zs xs≈ys = ≈-trans xs≈ys ys≈zs
+  step-≈-⟩ xs ys≈zs xs≈ys = ≈-trans xs≈ys ys≈zs
+
+  step-≈-⟨ : ∀ .{n≡m : n ≡ m}.{m≡o : m ≡ o} (xs : Vec A m) {ys : Vec A n} {zs : Vec A o} →
+           ys ≈[ trans n≡m m≡o ] zs → ys ≈[ n≡m ] xs → xs ≈[ m≡o ] zs
+  step-≈-⟨ xs ys≈zs ys≈xs = step-≈-⟩ xs ys≈zs (≈-sym ys≈xs)
 
   -- composition of the equality type on the right-hand side of _≈[_]_,
   -- or escaping to ordinary _≡_
-  step-≃ : ∀ .{m≡n : m ≡ n} (xs : Vec A m) {ys zs} → ys ≡ zs → xs ≈[ m≡n ] ys → xs ≈[ m≡n ] zs
-  step-≃ xs ys≡zs xs≈ys = ≈-trans xs≈ys (≈-reflexive ys≡zs)
+  step-≃-⟩ : ∀ .{m≡n : m ≡ n} (xs : Vec A m) {ys zs} → ys ≡ zs → xs ≈[ m≡n ] ys → xs ≈[ m≡n ] zs
+  step-≃-⟩ xs ys≡zs xs≈ys = ≈-trans xs≈ys (≈-reflexive ys≡zs)
+
+  step-≃-⟨ : ∀ .{m≡n : m ≡ n} (xs : Vec A m) {ys zs} → ys ≡ zs → ys ≈[ sym m≡n ] xs → xs ≈[ m≡n ] zs
+  step-≃-⟨ xs ys≡zs ys≈xs = step-≃-⟩ xs ys≡zs (≈-sym ys≈xs)
 
   -- composition of the equality type on the left-hand side of _≈[_]_
-  step-≂ : ∀ .{m≡n : m ≡ n} (xs : Vec A m) {ys zs} → ys ≈[ m≡n ] zs → xs ≡ ys → xs ≈[ m≡n ] zs
-  step-≂ xs ys≈zs xs≡ys = ≈-trans (≈-reflexive xs≡ys) ys≈zs
+  step-≂-⟩ : ∀ .{m≡n : m ≡ n} (xs : Vec A m) {ys zs} → ys ≈[ m≡n ] zs → xs ≡ ys → xs ≈[ m≡n ] zs
+  step-≂-⟩ xs ys≈zs xs≡ys = ≈-trans (≈-reflexive xs≡ys) ys≈zs
+
+  step-≂-⟨ : ∀ .{m≡n : m ≡ n} (xs : Vec A m) {ys zs} → ys ≈[ m≡n ] zs → ys ≡ xs → xs ≈[ m≡n ] zs
+  step-≂-⟨ xs ys≈zs ys≡xs = step-≂-⟩ xs ys≈zs (sym ys≡xs)
 
   -- `cong` after a `_≈[_]_` step that exposes the `cast` to the `cong`
   -- operation
@@ -103,29 +113,16 @@ module CastReasoning where
            xs ≈[ m≡n ] f (cast l≡o ys) → ys ≈[ l≡o ] zs → xs ≈[ m≡n ] f zs
   ≈-cong f xs≈fys ys≈zs = trans xs≈fys (cong f ys≈zs)
 
-
-  -- symmetric version of each of the operator
-  step-≈˘ : ∀ .{n≡m : n ≡ m}.{m≡o : m ≡ o} (xs : Vec A m) {ys : Vec A n} {zs : Vec A o} →
-           ys ≈[ trans n≡m m≡o ] zs → ys ≈[ n≡m ] xs → xs ≈[ m≡o ] zs
-  step-≈˘ xs ys≈zs ys≈xs = step-≈ xs ys≈zs (≈-sym ys≈xs)
-
-  step-≃˘ : ∀ .{m≡n : m ≡ n} (xs : Vec A m) {ys zs} → ys ≡ zs → ys ≈[ sym m≡n ] xs → xs ≈[ m≡n ] zs
-  step-≃˘ xs ys≡zs ys≈xs = step-≃ xs ys≡zs (≈-sym ys≈xs)
-
-  step-≂˘ : ∀ .{m≡n : m ≡ n} (xs : Vec A m) {ys zs} → ys ≈[ m≡n ] zs → ys ≡ xs → xs ≈[ m≡n ] zs
-  step-≂˘ xs ys≈zs ys≡xs = step-≂ xs ys≈zs (sym ys≡xs)
-
-
   ------------------------------------------------------------------------
   -- convenient syntax for ‘equational’ reasoning
 
   infix 1 begin_
-  infixr 2 step-≃ step-≂ step-≃˘ step-≂˘ step-≈ step-≈˘ _≈⟨⟩_ ≈-cong
+  infixr 2 step-≃-⟩ step-≃-⟨ step-≂-⟩ step-≂-⟨ step-≈-⟩ step-≈-⟨ _≈⟨⟩_ ≈-cong
   infix 3 _∎
 
-  syntax step-≃  xs ys≡zs xs≈ys  = xs ≃⟨  xs≈ys ⟩ ys≡zs
-  syntax step-≃˘ xs ys≡zs xs≈ys  = xs ≃˘⟨ xs≈ys ⟩ ys≡zs
-  syntax step-≂  xs ys≈zs xs≡ys  = xs ≂⟨  xs≡ys ⟩ ys≈zs
-  syntax step-≂˘ xs ys≈zs ys≡xs  = xs ≂˘⟨ ys≡xs ⟩ ys≈zs
-  syntax step-≈  xs ys≈zs xs≈ys  = xs ≈⟨  xs≈ys ⟩ ys≈zs
-  syntax step-≈˘ xs ys≈zs ys≈xs  = xs ≈˘⟨ ys≈xs ⟩ ys≈zs
+  syntax step-≃-⟩ xs ys≡zs xs≈ys  = xs ≃⟨ xs≈ys ⟩ ys≡zs
+  syntax step-≃-⟨ xs ys≡zs xs≈ys  = xs ≃⟨ xs≈ys ⟨ ys≡zs
+  syntax step-≂-⟩ xs ys≈zs xs≡ys  = xs ≂⟨ xs≡ys ⟩ ys≈zs
+  syntax step-≂-⟨ xs ys≈zs ys≡xs  = xs ≂⟨ ys≡xs ⟨ ys≈zs
+  syntax step-≈-⟩ xs ys≈zs xs≈ys  = xs ≈⟨ xs≈ys ⟩ ys≈zs
+  syntax step-≈-⟨ xs ys≈zs ys≈xs  = xs ≈⟨ ys≈xs ⟨ ys≈zs
diff --git a/src/Function/Properties/Surjection.agda b/src/Function/Properties/Surjection.agda
index d16670639c..d2aa85cd0f 100644
--- a/src/Function/Properties/Surjection.agda
+++ b/src/Function/Properties/Surjection.agda
@@ -58,7 +58,7 @@ injective⇒to⁻-cong : (surj : Surjection S T) →
 injective⇒to⁻-cong {T = T} surj injective {x} {y} x≈y = injective $ begin
   to (to⁻ x) ≈⟨ to∘to⁻ x ⟩
   x          ≈⟨ x≈y ⟩
-  y          ≈˘⟨ to∘to⁻ y ⟩
+  y          ≈⟨ to∘to⁻ y ⟨
   to (to⁻ y) ∎
   where
   open SetoidReasoning T
diff --git a/src/Relation/Binary/Construct/Closure/ReflexiveTransitive/Properties.agda b/src/Relation/Binary/Construct/Closure/ReflexiveTransitive/Properties.agda
index 58b2ee198a..a78d14938b 100644
--- a/src/Relation/Binary/Construct/Closure/ReflexiveTransitive/Properties.agda
+++ b/src/Relation/Binary/Construct/Closure/ReflexiveTransitive/Properties.agda
@@ -116,7 +116,7 @@ module StarReasoning {i t} {I : Set i} (T : Rel I t) where
   private module Base = PreorderReasoning (preorder T)
 
   open Base public
-    hiding (step-≈; step-∼; step-≲)
+    hiding (step-≈; step-≈˘; step-≈-⟩; step-≈-⟨; step-∼; step-≲)
     renaming (≲-go to ⟶-go)
 
   open ⟶-syntax _IsRelatedTo_ _IsRelatedTo_ (⟶-go ∘ (_◅ ε)) public
diff --git a/src/Relation/Binary/Construct/NaturalOrder/Right.agda b/src/Relation/Binary/Construct/NaturalOrder/Right.agda
index 80901f5939..3c2aa348d6 100644
--- a/src/Relation/Binary/Construct/NaturalOrder/Right.agda
+++ b/src/Relation/Binary/Construct/NaturalOrder/Right.agda
@@ -53,7 +53,7 @@ antisym : IsEquivalence _≈_ → Commutative _∙_ → Antisymmetric _≈_ _≤
 antisym isEq comm {x} {y} x≤y y≤x = begin
   x     ≈⟨  x≤y ⟩
   y ∙ x ≈⟨  comm y x ⟩
-  x ∙ y ≈˘⟨ y≤x ⟩
+  x ∙ y ≈⟨ y≤x ⟨
   y     ∎
   where open EqReasoning (record { isEquivalence = isEq })
 
diff --git a/src/Relation/Binary/HeterogeneousEquality.agda b/src/Relation/Binary/HeterogeneousEquality.agda
index 4581514feb..9181229eec 100644
--- a/src/Relation/Binary/HeterogeneousEquality.agda
+++ b/src/Relation/Binary/HeterogeneousEquality.agda
@@ -255,15 +255,23 @@ module ≅-Reasoning where
   -- Can't create syntax in the standard `Syntax` module for
   -- heterogeneous steps because it would force that module to use
   -- the `--with-k` option.
-  infixr 2 _≅⟨_⟩_ _≅˘⟨_⟩_
+  infixr 2 _≅⟨_⟩_ _≅⟨_⟨_
 
   _≅⟨_⟩_ : ∀ (x : A) {y : B} {z : C} →
            x ≅ y → y IsRelatedTo z → x IsRelatedTo z
   _ ≅⟨ x≅y ⟩ relTo y≅z = relTo (trans x≅y y≅z)
 
-  _≅˘⟨_⟩_ : ∀ (x : A) {y : B} {z : C} →
+  _≅⟨_⟨_ : ∀ (x : A) {y : B} {z : C} →
             y ≅ x → y IsRelatedTo z → x IsRelatedTo z
-  _ ≅˘⟨ y≅x ⟩ relTo y≅z = relTo (trans (sym y≅x) y≅z)
+  _ ≅⟨ y≅x ⟨ relTo y≅z = relTo (trans (sym y≅x) y≅z)
+
+  -- Deprecated
+  infixr 2 _≅˘⟨_⟩_
+  _≅˘⟨_⟩_ = _≅⟨_⟨_
+  {-# WARNING_ON_USAGE _≅˘⟨_⟩_
+  "Warning: _≅˘⟨_⟩_ was deprecated in v2.0.
+  Please use _≅⟨_⟨_ instead."
+  #-}
 
 ------------------------------------------------------------------------
 -- Inspect
diff --git a/src/Relation/Binary/Reasoning/PartialOrder.agda b/src/Relation/Binary/Reasoning/PartialOrder.agda
index 9dbf2fc712..b633f1f548 100644
--- a/src/Relation/Binary/Reasoning/PartialOrder.agda
+++ b/src/Relation/Binary/Reasoning/PartialOrder.agda
@@ -27,8 +27,8 @@
 --      w  <⟨ w<x ⟩
 --      x  ≤⟨ x≤y ⟩
 --      y  <⟨ y<z ⟩
---      z  ≡˘⟨ d≡z ⟩
---      d  ≈˘⟨ e≈d ⟩
+--      z  ≡⟨ d≡z ⟨
+--      d  ≈⟨ e≈d ⟨
 --      e  ∎
 --
 --    u≈w : u ≈ w
diff --git a/src/Relation/Binary/Reasoning/Preorder.agda b/src/Relation/Binary/Reasoning/Preorder.agda
index 933e8f0a45..aca729acc0 100644
--- a/src/Relation/Binary/Reasoning/Preorder.agda
+++ b/src/Relation/Binary/Reasoning/Preorder.agda
@@ -18,7 +18,7 @@
 --    u≈w = begin-equality
 --      u  ≈⟨ u≈v ⟩
 --      v  ≡⟨ v≡w ⟩
---      w  ≡˘⟨ x≡w ⟩
+--      w  ≡⟨ x≡w ⟨
 --      x  ∎
 
 {-# OPTIONS --cubical-compatible --safe #-}
diff --git a/src/Relation/Binary/Reasoning/Setoid.agda b/src/Relation/Binary/Reasoning/Setoid.agda
index bce0a3075c..ba6be9f79e 100644
--- a/src/Relation/Binary/Reasoning/Setoid.agda
+++ b/src/Relation/Binary/Reasoning/Setoid.agda
@@ -35,7 +35,9 @@ import Relation.Binary.Reasoning.Base.Single _≈_ refl trans
 
 -- Export the combinators for single relation reasoning, hiding the
 -- single misnamed combinator.
-open SingleRelReasoning public hiding (step-∼)
+open SingleRelReasoning public
+  hiding (step-∼)
+  renaming (∼-go to ≈-go)
 
 -- Re-export the equality-based combinators instead
-open ≈-syntax _IsRelatedTo_ _IsRelatedTo_ SingleRelReasoning.∼-go sym public
+open ≈-syntax _IsRelatedTo_ _IsRelatedTo_ ≈-go sym public
diff --git a/src/Relation/Binary/Reasoning/StrictPartialOrder.agda b/src/Relation/Binary/Reasoning/StrictPartialOrder.agda
index 2317ba4216..ad23a68481 100644
--- a/src/Relation/Binary/Reasoning/StrictPartialOrder.agda
+++ b/src/Relation/Binary/Reasoning/StrictPartialOrder.agda
@@ -28,8 +28,8 @@
 --      w  <⟨ w<x ⟩
 --      x  ≤⟨ x≤y ⟩
 --      y  <⟨ y<z ⟩
---      z  ≡˘⟨ d≡z ⟩
---      d  ≈˘⟨ e≈d ⟩
+--      z  ≡⟨ d≡z ⟨
+--      d  ≈⟨ e≈d ⟨
 --      e  ∎
 --
 --    u≈w : u ≈ w
diff --git a/src/Relation/Binary/Reasoning/Syntax.agda b/src/Relation/Binary/Reasoning/Syntax.agda
index e8286bee30..4806512296 100644
--- a/src/Relation/Binary/Reasoning/Syntax.agda
+++ b/src/Relation/Binary/Reasoning/Syntax.agda
@@ -23,7 +23,6 @@ open import Relation.Binary.PropositionalEquality.Core as P
 --   Effect/Monad/Partiality
 --   Effect/Monad/Partiality/All
 --   Codata/Guarded/Stream/Relation/Binary/Pointwise
---   Codata/Sized/Stream/Bisimilarity
 --   Function/Reasoning
 
 module Relation.Binary.Reasoning.Syntax where
@@ -259,37 +258,80 @@ module _
 
     -- Setoid equality syntax
     module ≈-syntax where
+      infixr 2 step-≈-⟩ step-≈-⟨
+      step-≈-⟩ = forward
+      step-≈-⟨ = backward
+      syntax step-≈-⟩ x yRz x≈y = x ≈⟨ x≈y ⟩ yRz
+      syntax step-≈-⟨ x yRz y≈x = x ≈⟨ y≈x ⟨ yRz
+
+      -- Deprecated
       infixr 2 step-≈ step-≈˘
-      step-≈ = forward
-      step-≈˘ = backward
-      syntax step-≈  x yRz x≈y = x ≈⟨ x≈y ⟩ yRz
+      step-≈ = step-≈-⟩
+      {-# WARNING_ON_USAGE step-≈
+      "Warning: step-≈ was deprecated in v2.0.
+      Please use step-≈-⟩ instead."
+      #-}
+      step-≈˘ = step-≈-⟨
+      {-# WARNING_ON_USAGE step-≈˘
+      "Warning: step-≈˘ and _≈˘⟨_⟩_ was deprecated in v2.0.
+      Please use step-≈-⟨ and _≈⟨_⟨_ instead."
+      #-}
       syntax step-≈˘ x yRz y≈x = x ≈˘⟨ y≈x ⟩ yRz
 
 
     -- Container equality syntax
     module ≋-syntax where
+      infixr 2 step-≋-⟩ step-≋-⟨
+      step-≋-⟩ = forward
+      step-≋-⟨ = backward
+      syntax step-≋-⟩ x yRz x≋y = x ≋⟨ x≋y ⟩ yRz
+      syntax step-≋-⟨ x yRz y≋x = x ≋⟨ y≋x ⟨ yRz
+
+
+      -- Don't remove until https://github.com/agda/agda/issues/5617 fixed.
       infixr 2 step-≋ step-≋˘
-      step-≋ = forward
-      step-≋˘ = backward
-      syntax step-≋  x yRz x≋y = x ≋⟨ x≋y ⟩ yRz
+      step-≋ = step-≋-⟩
+      {-# WARNING_ON_USAGE step-≋
+      "Warning: step-≋ was deprecated in v2.0.
+      Please use step-≋-⟩ instead."
+      #-}
+      step-≋˘ = step-≋-⟨
+      {-# WARNING_ON_USAGE step-≋˘
+      "Warning: step-≋˘ and _≋˘⟨_⟩_ was deprecated in v2.0.
+      Please use step-≋-⟨ and _≋⟨_⟨_ instead."
+      #-}
       syntax step-≋˘ x yRz y≋x = x ≋˘⟨ y≋x ⟩ yRz
 
 
     -- Other equality syntax
     module ≃-syntax where
-      infixr 2 step-≃ step-≃˘
-      step-≃ = forward
-      step-≃˘ = backward
-      syntax step-≃  x yRz x≃y = x ≃⟨ x≃y ⟩ yRz
-      syntax step-≃˘ x yRz y≃x = x ≃˘⟨ y≃x ⟩ yRz
+      infixr 2 step-≃-⟩ step-≃-⟨
+      step-≃-⟩ = forward
+      step-≃-⟨ = backward
+      syntax step-≃-⟩ x yRz x≃y = x ≃⟨ x≃y ⟩ yRz
+      syntax step-≃-⟨ x yRz y≃x = x ≃⟨ y≃x ⟨ yRz
 
 
     -- Apartness relation syntax
     module #-syntax where
+      infixr 2 step-#-⟩ step-#-⟨
+      step-#-⟩ = forward
+      step-#-⟨ = backward
+      syntax step-#-⟩ x yRz x#y = x #⟨ x#y ⟩ yRz
+      syntax step-#-⟨ x yRz y#x = x #⟨ y#x ⟨ yRz
+
+      -- Don't remove until https://github.com/agda/agda/issues/5617 fixed.
       infixr 2 step-# step-#˘
-      step-# = forward
-      step-#˘ = backward
-      syntax step-#  x yRz x#y = x #⟨ x#y ⟩ yRz
+      step-# = step-#-⟩
+      {-# WARNING_ON_USAGE step-#
+      "Warning: step-# was deprecated in v2.0.
+      Please use step-#-⟩ instead."
+      #-}
+      step-#˘ = step-#-⟨
+      {-# WARNING_ON_USAGE step-#˘
+      "Warning: step-#˘ and _#˘⟨_⟩_ was deprecated in v2.0.
+      Please use step-#-⟨ and _#⟨_⟨_ instead."
+      #-}
       syntax step-#˘ x yRz y#x = x #˘⟨ y#x ⟩ yRz
 
 
@@ -304,20 +346,35 @@ module _
 
     -- Inverse syntax
     module ↔-syntax where
-      infixr 2 step-↔ step-↔-sym
-      step-↔ = forward
-      step-↔-sym = backward
-      syntax step-↔ x yRz x↔y = x ↔⟨ x↔y ⟩ yRz
-      syntax step-↔-sym x yRz y↔x = x ↔˘⟨ y↔x ⟩ yRz
+      infixr 2 step-↔-⟩ step-↔-⟨
+      step-↔-⟩ = forward
+      step-↔-⟨ = backward
+      syntax step-↔-⟩ x yRz x↔y = x ↔⟨ x↔y ⟩ yRz
+      syntax step-↔-⟨ x yRz y↔x = x ↔⟨ y↔x ⟨ yRz
 
 
     -- Inverse syntax
     module ↭-syntax where
-      infixr 2 step-↭ step-↭-sym
+      infixr 2 step-↭-⟩ step-↭-⟨
+      step-↭-⟩ = forward
+      step-↭-⟨ = backward
+      syntax step-↭-⟩ x yRz x↭y = x ↭⟨ x↭y ⟩ yRz
+      syntax step-↭-⟨ x yRz y↭x = x ↭⟨ y↭x ⟨ yRz
+
+
+      -- Don't remove until https://github.com/agda/agda/issues/5617 fixed.
+      infixr 2 step-↭ step-↭˘
       step-↭ = forward
-      step-↭-sym = backward
-      syntax step-↭ x yRz x↭y = x ↭⟨ x↭y ⟩ yRz
-      syntax step-↭-sym x yRz y↭x = x ↭˘⟨ y↭x ⟩ yRz
+      {-# WARNING_ON_USAGE step-↭
+      "Warning: step-↭ was deprecated in v2.0.
+      Please use step-↭-⟩ instead."
+      #-}
+      step-↭˘ = backward
+      {-# WARNING_ON_USAGE step-↭˘
+      "Warning: step-↭˘ and _↭˘⟨_⟩_ was deprecated in v2.0.
+      Please use step-↭-⟨ and _↭⟨_⟨_ instead."
+      #-}
+      syntax step-↭˘ x yRz y↭x = x ↭˘⟨ y↭x ⟩ yRz
 
 ------------------------------------------------------------------------
 -- Propositional equality
@@ -332,16 +389,32 @@ module ≡-syntax
   (step : Trans _≡_ R R)
   where
 
-  infixr 2 step-≡ step-≡-refl step-≡˘
-  step-≡ = forward R R step
-  step-≡˘ = backward R R step P.sym
+  infixr 2 step-≡-⟩  step-≡-∣ step-≡-⟨
+  step-≡-⟩ = forward R R step
+
+  step-≡-∣ : ∀ x {y} → R x y → R x y
+  step-≡-∣ x xRy = xRy
+
+  step-≡-⟨ = backward R R step P.sym
+
+  syntax step-≡-⟩ x yRz x≡y = x ≡⟨ x≡y ⟩ yRz
+  syntax step-≡-∣ x xRy     = x ≡⟨⟩ xRy
+  syntax step-≡-⟨ x yRz y≡x = x ≡⟨ y≡x ⟨ yRz
 
-  step-≡-refl : ∀ x {y} → R x y → R x y
-  step-≡-refl x xRy = xRy
 
-  syntax step-≡-refl x xRy     = x ≡⟨⟩ xRy
-  syntax step-≡˘     x yRz y≡x = x ≡˘⟨ y≡x ⟩ yRz
-  syntax step-≡      x yRz x≡y = x ≡⟨ x≡y ⟩ yRz
+  -- Don't remove until https://github.com/agda/agda/issues/5617 fixed.
+  infixr 2 step-≡ step-≡˘
+  step-≡ = step-≡-⟩
+  {-# WARNING_ON_USAGE step-≡
+  "Warning: step-≡ was deprecated in v2.0.
+  Please use step-≡-⟩ instead."
+  #-}
+  step-≡˘ = step-≡-⟨
+  {-# WARNING_ON_USAGE step-≡˘
+  "Warning: step-≡˘ and _≡˘⟨_⟩_ was deprecated in v2.0.
+  Please use step-≡-⟨ and _≡⟨_⟨_ instead."
+  #-}
+  syntax step-≡˘ x yRz y≡x = x ≡˘⟨ y≡x ⟩ yRz
 
 
 -- Unlike ≡-syntax above, chains of reasoning using this syntax will not
diff --git a/src/Tactic/Cong.agda b/src/Tactic/Cong.agda
index b7accfcc08..2c1b4196b1 100644
--- a/src/Tactic/Cong.agda
+++ b/src/Tactic/Cong.agda
@@ -15,7 +15,7 @@
 --     suc (suc m) + m
 --   ≡⟨ cong! eq ⟩
 --     suc (suc n) + n
---   ≡˘⟨ cong! (+-identityʳ n) ⟩
+--   ≡⟨ cong! (+-identityʳ n) ⟨
 --     suc (suc n) + (n + 0)
 --   ∎
 ------------------------------------------------------------------------
diff --git a/src/Tactic/MonoidSolver.agda b/src/Tactic/MonoidSolver.agda
index c137e44990..c62ea9dccf 100644
--- a/src/Tactic/MonoidSolver.agda
+++ b/src/Tactic/MonoidSolver.agda
@@ -132,7 +132,7 @@ module _ {m₁ m₂} (monoid : Monoid m₁ m₂) where
   homo′ [ x ↑] y   = ∙-congʳ (identityʳ x)
   homo′ (x ∙′ y) z = begin
     [ x ∙′ y ⇓] ∙ z       ≡⟨⟩
-    [ x ⇓]′ [ y ⇓] ∙ z    ≈˘⟨ ∙-congʳ (homo′ x [ y ⇓]) ⟩
+    [ x ⇓]′ [ y ⇓] ∙ z    ≈⟨ ∙-congʳ (homo′ x [ y ⇓]) ⟨
     ([ x ⇓] ∙ [ y ⇓]) ∙ z ≈⟨ assoc [ x ⇓] [ y ⇓] z ⟩
     [ x ⇓] ∙ ([ y ⇓] ∙ z) ≈⟨ ∙-congˡ (homo′ y z) ⟩
     [ x ⇓] ∙ ([ y ⇓]′ z)  ≈⟨ homo′ x ([ y ⇓]′ z) ⟩
@@ -143,7 +143,7 @@ module _ {m₁ m₂} (monoid : Monoid m₁ m₂) where
   homo [ x ↑]   = identityʳ x
   homo (x ∙′ y) = begin
     [ x ∙′ y ⇓]     ≡⟨⟩
-    [ x ⇓]′ [ y ⇓]  ≈˘⟨ homo′ x [ y ⇓] ⟩
+    [ x ⇓]′ [ y ⇓]  ≈⟨ homo′ x [ y ⇓] ⟨
     [ x ⇓] ∙ [ y ⇓] ≈⟨ ∙-cong (homo x) (homo y) ⟩
     [ x ↓] ∙ [ y ↓] ∎
 
diff --git a/src/Tactic/RingSolver/Core/Polynomial/Homomorphism/Lemmas.agda b/src/Tactic/RingSolver/Core/Polynomial/Homomorphism/Lemmas.agda
index 4bdfd74381..f014d54c9f 100644
--- a/src/Tactic/RingSolver/Core/Polynomial/Homomorphism/Lemmas.agda
+++ b/src/Tactic/RingSolver/Core/Polynomial/Homomorphism/Lemmas.agda
@@ -246,7 +246,7 @@ poly-foldR ρ ρs f e cng dist step base (x ≠0 Δ suc i & []) =
     ⅀?⟦ y Δ suc i ∷↓ ys ⟧ (ρ , ρs)
   ≈⟨ ∷↓-hom-s y i ys ρ ρs ⟩
     (ρ ^ suc i) * ((y , ys) ⟦∷⟧ (ρ , ρs))
-  ≈˘⟨ *≫ ⟦∷⟧?-hom y ys ρ ρs ⟩
+  ≈⟨ *≫ ⟦∷⟧?-hom y ys ρ ρs ⟨
     (ρ ^ suc i) * ((y , ys) ⟦∷⟧? (ρ , ρs))
   ≈⟨ *≫ step x [] (sym base) ⟩
     (ρ ^ suc i) * e ((x , []) ⟦∷⟧? (ρ , ρs))
@@ -265,7 +265,7 @@ poly-foldR ρ ρs f e cng dist step base (x ≠0 Δ suc i & ∹ xs) =
     ⅀?⟦ y Δ suc i ∷↓ zs ⟧ (ρ , ρs)
   ≈⟨ ∷↓-hom-s y i zs ρ ρs ⟩
     (ρ ^ suc i) * ((y , zs) ⟦∷⟧ (ρ , ρs))
-  ≈˘⟨ *≫ ⟦∷⟧?-hom y zs ρ ρs ⟩
+  ≈⟨ *≫ ⟦∷⟧?-hom y zs ρ ρs ⟨
     (ρ ^ suc i) * ((y , zs) ⟦∷⟧? (ρ , ρs))
   ≈⟨ *≫ step x (∹ xs) (poly-foldR ρ ρs f e cng dist step base xs) ⟩
     (ρ ^ suc i) * e ((x , (∹ xs )) ⟦∷⟧? (ρ , ρs))
@@ -283,7 +283,7 @@ poly-foldR ρ ρs f e cng dist step base (x ≠0 Δ ℕ.zero & []) =
     ⅀?⟦ y Δ ℕ.zero ∷↓ zs ⟧ (ρ , ρs)
   ≈⟨ ∷↓-hom-0 y zs ρ ρs ⟩
     ((y , zs) ⟦∷⟧ (ρ , ρs))
-  ≈˘⟨ ⟦∷⟧?-hom y zs ρ ρs ⟩
+  ≈⟨ ⟦∷⟧?-hom y zs ρ ρs ⟨
     ((y , zs) ⟦∷⟧? (ρ , ρs))
   ≈⟨ step x [] (sym base) ⟩
     e ((x , []) ⟦∷⟧? (ρ , ρs))
@@ -300,7 +300,7 @@ poly-foldR ρ ρs f e cng dist step base (x ≠0 Δ ℕ.zero & (∹ xs )) =
     ⅀?⟦ y Δ ℕ.zero ∷↓ zs ⟧ (ρ , ρs)
   ≈⟨ ∷↓-hom-0 y zs ρ ρs ⟩
     ((y , zs) ⟦∷⟧ (ρ , ρs))
-  ≈˘⟨ ⟦∷⟧?-hom y zs ρ ρs ⟩
+  ≈⟨ ⟦∷⟧?-hom y zs ρ ρs ⟨
     ((y , zs) ⟦∷⟧? (ρ , ρs))
   ≈⟨ step x (∹ xs ) (poly-foldR ρ ρs f e cng dist step base xs) ⟩
     e ((x , (∹ xs )) ⟦∷⟧ (ρ , ρs))
diff --git a/src/Text/Pretty/Core.agda b/src/Text/Pretty/Core.agda
index 974b1af823..96415feb7f 100644
--- a/src/Text/Pretty/Core.agda
+++ b/src/Text/Pretty/Core.agda
@@ -190,7 +190,7 @@ private
     isBlock ∣x∣ ∣y∣ with blocky
     ... | nothing        = begin
       size blockx         ≡⟨ ∣x∣ ⟩
-      x.height            ≡˘⟨ +-identityʳ x.height ⟩
+      x.height            ≡⟨ +-identityʳ x.height ⟨
       x.height + 0        ≡⟨ cong (_ +_) ∣y∣ ⟩
       x.height + y.height ∎ where open ≡-Reasoning
     ... | just (hd , tl) = begin