diff --git a/library/standard/logic/connectives/basic.lean b/library/standard/logic/connectives/basic.lean index 3a8a30e22..0fd2ecf28 100644 --- a/library/standard/logic/connectives/basic.lean +++ b/library/standard/logic/connectives/basic.lean @@ -153,12 +153,12 @@ theorem iff_intro {a b : Prop} (H1 : a → b) (H2 : b → a) : a ↔ b := and_in theorem iff_elim {a b c : Prop} (H1 : (a → b) → (b → a) → c) (H2 : a ↔ b) : c := and_rec H1 H2 -theorem iff_elim_left ⦃a b : Prop⦄ (H : a ↔ b) : a → b := +theorem iff_elim_left {a b : Prop} (H : a ↔ b) : a → b := iff_elim (assume H1 H2, H1) H -abbreviation iff_mp := iff_elim_left +abbreviation iff_mp := @iff_elim_left -theorem iff_elim_right ⦃a b : Prop⦄ (H : a ↔ b) : b → a := +theorem iff_elim_right {a b : Prop} (H : a ↔ b) : b → a := iff_elim (assume H1 H2, H2) H theorem iff_flip_sign {a b : Prop} (H1 : a ↔ b) : ¬a ↔ ¬b := @@ -169,12 +169,12 @@ iff_intro theorem iff_refl (a : Prop) : a ↔ a := iff_intro (assume H, H) (assume H, H) -theorem iff_trans ⦃a b c : Prop⦄ (H1 : a ↔ b) (H2 : b ↔ c) : a ↔ c := +theorem iff_trans {a b c : Prop} (H1 : a ↔ b) (H2 : b ↔ c) : a ↔ c := iff_intro (assume Ha, iff_elim_left H2 (iff_elim_left H1 Ha)) (assume Hc, iff_elim_right H1 (iff_elim_right H2 Hc)) -theorem iff_symm ⦃a b : Prop⦄ (H : a ↔ b) : b ↔ a := +theorem iff_symm {a b : Prop} (H : a ↔ b) : b ↔ a := iff_intro (assume Hb, iff_elim_right H Hb) (assume Ha, iff_elim_left H Ha) diff --git a/library/standard/logic/connectives/instances.lean b/library/standard/logic/connectives/instances.lean index 79702797e..6101ed0ff 100644 --- a/library/standard/logic/connectives/instances.lean +++ b/library/standard/logic/connectives/instances.lean @@ -111,7 +111,7 @@ relation.mp_like_mk (iff_elim_left H) -- Substition for iff -- ------------------ -theorem subst_iff ⦃P : Prop → Prop⦄ {C : congr iff iff P} {a b : Prop} (H : a ↔ b) (H1 : P a) : +theorem subst_iff {P : Prop → Prop} {C : congr iff iff P} {a b : Prop} (H : a ↔ b) (H1 : P a) : P b := @general_operations.subst Prop iff P C a b H H1 @@ -124,14 +124,14 @@ calc_trans iff_trans calc_subst subst_iff namespace iff_ops - postfix `⁻¹`:100 := iff_symm - infixr `⬝`:75 := iff_trans - infixr `▸`:75 := subst_iff - abbreviation refl := iff_refl - abbreviation symm := iff_symm - abbreviation trans := iff_trans - abbreviation subst := subst_iff - abbreviation mp := iff_mp + postfix `⁻¹`:100 := iff_symm + infixr `⬝`:75 := iff_trans + infixr `▸`:75 := subst_iff + abbreviation refl := iff_refl + abbreviation symm := @iff_symm + abbreviation trans := @iff_trans + abbreviation subst := @subst_iff + abbreviation mp := @iff_mp end iff_ops