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[Merged by Bors] - feat(topology/basic): intersection of a finset-indexed open sets is open #16075

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[Merged by Bors] - feat(topology/basic): intersection of a finset-indexed open sets is open #16075

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4 changes: 4 additions & 0 deletions src/topology/basic.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -147,6 +147,10 @@ lemma is_open_Inter_prop {p : Prop} {s : p → set α}
(h : ∀ h : p, is_open (s h)) : is_open (Inter s) :=
by by_cases p; simp *

lemma is_open_bInter_finset {s : finset β} {f : β → set α} (h : ∀ i ∈ s, is_open (f i)) :
is_open (⋂ i ∈ s, f i) :=
is_open_bInter (to_finite _) h

lemma is_open_const {p : Prop} : is_open {a : α | p} :=
by_cases
(assume : p, begin simp only [this]; exact is_open_univ end)
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