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chore(order/filter/basic): add 2 trivial simp lemmas (#10344)
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urkud committed Nov 16, 2021
1 parent 1181c99 commit f01399c
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5 changes: 5 additions & 0 deletions src/order/filter/basic.lean
Expand Up @@ -888,6 +888,8 @@ notation `∀ᶠ` binders ` in ` f `, ` r:(scoped p, filter.eventually p f) := r
lemma eventually_iff {f : filter α} {P : α → Prop} : (∀ᶠ x in f, P x) ↔ {x | P x} ∈ f :=
iff.rfl

@[simp] lemma eventually_mem_set {s : set α} {l : filter α} : (∀ᶠ x in l, x ∈ s) ↔ s ∈ l := iff.rfl

protected lemma ext' {f₁ f₂ : filter α}
(h : ∀ p : α → Prop, (∀ᶠ x in f₁, p x) ↔ (∀ᶠ x in f₂, p x)) :
f₁ = f₂ :=
Expand Down Expand Up @@ -1188,6 +1190,9 @@ eventually_congr $ eventually_of_forall $ λ x, ⟨eq.to_iff, iff.to_eq⟩

alias eventually_eq_set ↔ filter.eventually_eq.mem_iff filter.eventually.set_eq

@[simp] lemma eventually_eq_univ {s : set α} {l : filter α} : s =ᶠ[l] univ ↔ s ∈ l :=
by simp [eventually_eq_set]

lemma eventually_eq.exists_mem {l : filter α} {f g : α → β} (h : f =ᶠ[l] g) :
∃ s ∈ l, eq_on f g s :=
h.exists_mem
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