@@ -646,6 +646,10 @@ theorem eventually_or_distrib_right {f : Filter α} {p : α → Prop} {q : Prop}
646646 (∀ᶠ x in f, p x ∨ q) ↔ (∀ᶠ x in f, p x) ∨ q := by
647647 simp only [@or_comm _ q, eventually_or_distrib_left]
648648
649+ theorem eventually_imp_distrib_left {f : Filter α} {p : Prop } {q : α → Prop } :
650+ (∀ᶠ x in f, p → q x) ↔ p → ∀ᶠ x in f, q x := by
651+ simp only [imp_iff_not_or, eventually_or_distrib_left]
652+
649653@[simp]
650654theorem eventually_bot {p : α → Prop } : ∀ᶠ x in ⊥, p x :=
651655 ⟨⟩
@@ -798,6 +802,16 @@ theorem eventually_imp_distrib_right {f : Filter α} {p : α → Prop} {q : Prop
798802 (∀ᶠ x in f, p x → q) ↔ (∃ᶠ x in f, p x) → q := by
799803 simp only [imp_iff_not_or, eventually_or_distrib_right, not_frequently]
800804
805+ @[simp]
806+ theorem frequently_and_distrib_left {f : Filter α} {p : Prop } {q : α → Prop } :
807+ (∃ᶠ x in f, p ∧ q x) ↔ p ∧ ∃ᶠ x in f, q x := by
808+ simp only [Filter.Frequently, not_and, eventually_imp_distrib_left, Classical.not_imp]
809+
810+ @[simp]
811+ theorem frequently_and_distrib_right {f : Filter α} {p : α → Prop } {q : Prop } :
812+ (∃ᶠ x in f, p x ∧ q) ↔ (∃ᶠ x in f, p x) ∧ q := by
813+ simp only [@and_comm _ q, frequently_and_distrib_left]
814+
801815@[simp]
802816theorem frequently_bot {p : α → Prop } : ¬∃ᶠ x in ⊥, p x := by simp
803817
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