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chore(order/filter): add 2 lemmas (#9682)
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urkud committed Oct 13, 2021
1 parent 8886386 commit 4c1a9c4
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8 changes: 8 additions & 0 deletions src/order/filter/basic.lean
Expand Up @@ -1135,6 +1135,14 @@ by simp
(∀ᶠ x in f, p x → q) ↔ ((∃ᶠ x in f, p x) → q) :=
by simp only [imp_iff_not_or, eventually_or_distrib_right, not_frequently]

@[simp] lemma frequently_and_distrib_left {f : filter α} {p : Prop} {q : α → Prop} :
(∃ᶠ x in f, p ∧ q x) ↔ (p ∧ ∃ᶠ x in f, q x) :=
by simp only [filter.frequently, not_and, eventually_imp_distrib_left, not_imp]

@[simp] lemma frequently_and_distrib_right {f : filter α} {p : α → Prop} {q : Prop} :
(∃ᶠ x in f, p x ∧ q) ↔ ((∃ᶠ x in f, p x) ∧ q) :=
by simp only [and_comm _ q, frequently_and_distrib_left]

@[simp] lemma frequently_bot {p : α → Prop} : ¬ ∃ᶠ x in ⊥, p x := by simp

@[simp]
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