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continuous_big
#1706
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I am a bit surprised to see a mix of |
theories/function_spaces.v
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Lemma cvg_big (T : Type) (U : topologicalType) [F : set_system T] [I : Type] | ||
(r : seq I) (P : pred I) (Ff : I -> T -> U) (Fa : I -> U) | ||
(op : U -> U -> U) (x0 : U): |
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(op : U -> U -> U) (x0 : U): | |
(op : U -> U -> U) (x0 : U) : |
theories/function_spaces.v
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under eq_cvg do rewrite big_nil. | ||
exact: cvg_cst. | ||
rewrite big_cons (eq_cvg _ _ (fun x => big_cons _ _ _ _ _ _)). | ||
case/boolP: (P x) => // Px. |
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case/boolP: (P x) => // Px. | |
case: ifPn => // Px. |
theories/function_spaces.v
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exact: cvg_cst. | ||
rewrite big_cons (eq_cvg _ _ (fun x => big_cons _ _ _ _ _ _)). | ||
case/boolP: (P x) => // Px. | ||
apply: (@cvg_comp _ _ _ (fun x1 => (Ff x x1, \big[op/x0]_(j <- r | P j) Ff j x1)) _ _ (nbhs (Fa x, \big[op/x0]_(j <- r | P j) Fa j)) _ _ (continuous_curry_cvg opC0)). |
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apply: (@cvg_comp _ _ _ (fun x1 => (Ff x x1, \big[op/x0]_(j <- r | P j) Ff j x1)) _ _ (nbhs (Fa x, \big[op/x0]_(j <- r | P j) Fa j)) _ _ (continuous_curry_cvg opC0)). | |
apply: (@cvg_comp _ _ _ | |
(fun x1 => (Ff x x1, \big[op/x0]_(j <- r | P j) Ff j x1)) _ _ | |
(nbhs (Fa x, \big[op/x0]_(j <- r | P j) Fa j)) _ _ | |
(continuous_curry_cvg opC0)). |
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Just because I couldn't read it easily ^_^
Also, since this is a section, we can maybe exploit some sharing with |
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That is an excellent question. I guess I saw other lemmas doing it and I assumed this was the way to go. |
Would that not mess with the order of the arguments? |
It will have an impact on it. What do you think? |
Co-authored-by: Reynald Affeldt <[email protected]>
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I took your commit, I am surprised you can not push on my branch. I am more convinced by uniformity of statements than sharing of arguments, but this is fine, I guess. The |
Co-authored-by: Reynald Affeldt <[email protected]>
Motivation for this change
A general continuity lemma for bigops.
Checklist
CHANGELOG_UNRELEASED.md
Reference: How to document
Merge policy
As a rule of thumb:
all compile are preferentially merged into master.
Reminder to reviewers