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[Merged by Bors] - feat: port Topology.ContinuousOn #1907

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[Merged by Bors] - feat: port Topology.ContinuousOn #1907

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@urkud urkud commented Jan 28, 2023

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@Ruben-VandeVelde Ruben-VandeVelde added blocked-by-other-PR This PR depends on another PR which is still in the queue. mathlib-port This is a port of a theory file from mathlib. labels Jan 28, 2023
@semorrison semorrison added merge-conflict The PR has a merge conflict with master, and needs manual merging. and removed blocked-by-other-PR This PR depends on another PR which is still in the queue. merge-conflict The PR has a merge conflict with master, and needs manual merging. labels Jan 28, 2023
@urkud
feat: port Topology.ContinuousOn
6cf3728
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Initial file copy from mathport
0b24c5a
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automated fixes
7a85181 
Mathbin -> Mathlib

fix certain import statements

move "by" to end of line

add import to Mathlib.lean
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Fix
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@urkud urkud added the awaiting-review The author would like community review of the PR label Jan 31, 2023
urkud
urkud commented Jan 31, 2023
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Mathlib/Topology/ContinuousOn.lean
#align nhds_within_le_iff nhdsWithin_le_iff

-- porting note: golfed, droped an unneeded assumption
theorem preimage_nhdsWithin_coinduced' {π : α → β} {s : Set β} {t : Set α} {a : α} (h : a ∈ t)
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@urkud urkud Jan 31, 2023 •
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I'm going to backport this and 1 similar change below.

urkud
urkud commented Jan 31, 2023
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Mathlib/Topology/ContinuousOn.lean
(hg x hx).congr (fun y hy => piecewise_eq_of_not_mem _ _ _ hy.2)
(piecewise_eq_of_not_mem _ _ _ hx.2)
#align continuous_on.piecewise' ContinuousOn.piecewise'

theorem ContinuousOn.if' {s : Set α} {p : α → Prop} {f g : α → β} [∀ a, Decidable (p a)]
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Lean failed to find a Decidable instance to apply the piecewise' version here, so I swapped the lemmas.

jcommelin
jcommelin reviewed Jan 31, 2023
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Mathlib/Topology/ContinuousOn.lean
@@ -306,15 +295,6 @@ theorem nhdsWithin_compl_singleton_sup_pure (a : α) : 𝓝[≠] a ⊔ pure a =
rw [← nhdsWithin_singleton, ← nhdsWithin_union, compl_union_self, nhdsWithin_univ]
#align nhds_within_compl_singleton_sup_pure nhdsWithin_compl_singleton_sup_pure

/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
theorem nhdsWithin_prod_eq {α : Type _} [TopologicalSpace α] {β : Type _} [TopologicalSpace β]
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What happened to this decl?

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@jcommelin It was moved to Topology.Constructions.

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Apparently it moved to Topology.Constructions.

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Thanks 🎉

bors merge

@github-actions github-actions bot added ready-to-merge This PR has been sent to bors. and removed awaiting-review The author would like community review of the PR labels Jan 31, 2023
bors bot pushed a commit that referenced this pull request Jan 31, 2023
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feat: port Topology.ContinuousOn (#1907)
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bors bot commented Jan 31, 2023

Pull request successfully merged into master.

Build succeeded:

@bors bors bot changed the title feat: port Topology.ContinuousOn [Merged by Bors] - feat: port Topology.ContinuousOn Jan 31, 2023
@bors bors bot closed this Jan 31, 2023
@bors bors bot deleted the port/Topology.ContinuousOn branch January 31, 2023 21:48
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