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Surjective と Injective の大文字小文字をMathlibに合わせる
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Seasawher committed Sep 24, 2024
1 parent 6696622 commit d879831
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8 changes: 4 additions & 4 deletions Examples/Solution/CantorTheorem.lean
Original file line number Diff line number Diff line change
Expand Up @@ -113,10 +113,10 @@ section --#
variable {α β : Type}

/-- 関数の全射性 -/
def Function.surjective (f : α → β) : Prop := ∀ b, ∃ a, f a = b
def Function.Surjective (f : α → β) : Prop := ∀ b, ∃ a, f a = b

/-- 関数の単射性 -/
def Function.injective (f : α → β) : Prop := ∀ {a₁ a₂ : α}, f a₁ = f a₂ → a₁ = a₂
def Function.Injective (f : α → β) : Prop := ∀ {a₁ a₂ : α}, f a₁ = f a₂ → a₁ = a₂

end --#
/-
Expand All @@ -141,7 +141,7 @@ variable {α : Type}
open Function

/-- ある集合からそのベキ集合への全射は存在しない -/
theorem cantor_surjective (f : α → Set α) : ¬ surjective f := by
theorem cantor_surjective (f : α → Set α) : ¬ Surjective f := by
-- `f` が全射であると仮定する
intro hsurj

Expand All @@ -165,7 +165,7 @@ theorem cantor_surjective (f : α → Set α) : ¬ surjective f := by
simp at this

/-- ベキ集合から元の集合への単射は存在しない -/
theorem cantor_injective (f : Set α → α) : ¬ injective f := by
theorem cantor_injective (f : Set α → α) : ¬ Injective f := by
-- `f` が単射だと仮定する
intro hinj

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8 changes: 4 additions & 4 deletions Exercise/CantorTheorem.lean
Original file line number Diff line number Diff line change
Expand Up @@ -113,10 +113,10 @@ section --#
variable {α β : Type}

/-- 関数の全射性 -/
def Function.surjective (f : α → β) : Prop := ∀ b, ∃ a, f a = b
def Function.Surjective (f : α → β) : Prop := ∀ b, ∃ a, f a = b

/-- 関数の単射性 -/
def Function.injective (f : α → β) : Prop := ∀ {a₁ a₂ : α}, f a₁ = f a₂ → a₁ = a₂
def Function.Injective (f : α → β) : Prop := ∀ {a₁ a₂ : α}, f a₁ = f a₂ → a₁ = a₂

end --#
/-
Expand All @@ -141,7 +141,7 @@ variable {α : Type}
open Function

/-- ある集合からそのベキ集合への全射は存在しない -/
theorem cantor_surjective (f : α → Set α) : ¬ surjective f := by
theorem cantor_surjective (f : α → Set α) : ¬ Surjective f := by
-- `f` が全射であると仮定する
intro hsurj

Expand All @@ -158,7 +158,7 @@ theorem cantor_surjective (f : α → Set α) : ¬ surjective f := by
simp at this

/-- ベキ集合から元の集合への単射は存在しない -/
theorem cantor_injective (f : Set α → α) : ¬ injective f := by
theorem cantor_injective (f : Set α → α) : ¬ Injective f := by
-- `f` が単射だと仮定する
intro hinj

Expand Down

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