refactor(library/standard): define abbreviations using '@'
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
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2 changed files with 14 additions and 14 deletions
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@ -153,12 +153,12 @@ theorem iff_intro {a b : Prop} (H1 : a → b) (H2 : b → a) : a ↔ b := and_in
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theorem iff_elim {a b c : Prop} (H1 : (a → b) → (b → a) → c) (H2 : a ↔ b) : c := and_rec H1 H2
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theorem iff_elim_left ⦃a b : Prop⦄ (H : a ↔ b) : a → b :=
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theorem iff_elim_left {a b : Prop} (H : a ↔ b) : a → b :=
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iff_elim (assume H1 H2, H1) H
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abbreviation iff_mp := iff_elim_left
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abbreviation iff_mp := @iff_elim_left
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theorem iff_elim_right ⦃a b : Prop⦄ (H : a ↔ b) : b → a :=
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theorem iff_elim_right {a b : Prop} (H : a ↔ b) : b → a :=
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iff_elim (assume H1 H2, H2) H
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theorem iff_flip_sign {a b : Prop} (H1 : a ↔ b) : ¬a ↔ ¬b :=
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@ -169,12 +169,12 @@ iff_intro
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theorem iff_refl (a : Prop) : a ↔ a :=
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iff_intro (assume H, H) (assume H, H)
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theorem iff_trans ⦃a b c : Prop⦄ (H1 : a ↔ b) (H2 : b ↔ c) : a ↔ c :=
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theorem iff_trans {a b c : Prop} (H1 : a ↔ b) (H2 : b ↔ c) : a ↔ c :=
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iff_intro
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(assume Ha, iff_elim_left H2 (iff_elim_left H1 Ha))
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(assume Hc, iff_elim_right H1 (iff_elim_right H2 Hc))
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theorem iff_symm ⦃a b : Prop⦄ (H : a ↔ b) : b ↔ a :=
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theorem iff_symm {a b : Prop} (H : a ↔ b) : b ↔ a :=
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iff_intro
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(assume Hb, iff_elim_right H Hb)
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(assume Ha, iff_elim_left H Ha)
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@ -111,7 +111,7 @@ relation.mp_like_mk (iff_elim_left H)
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-- Substition for iff
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-- ------------------
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theorem subst_iff ⦃P : Prop → Prop⦄ {C : congr iff iff P} {a b : Prop} (H : a ↔ b) (H1 : P a) :
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theorem subst_iff {P : Prop → Prop} {C : congr iff iff P} {a b : Prop} (H : a ↔ b) (H1 : P a) :
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P b :=
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@general_operations.subst Prop iff P C a b H H1
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@ -128,10 +128,10 @@ namespace iff_ops
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infixr `⬝`:75 := iff_trans
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infixr `▸`:75 := subst_iff
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abbreviation refl := iff_refl
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abbreviation symm := iff_symm
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abbreviation trans := iff_trans
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abbreviation subst := subst_iff
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abbreviation mp := iff_mp
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abbreviation symm := @iff_symm
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abbreviation trans := @iff_trans
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abbreviation subst := @subst_iff
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abbreviation mp := @iff_mp
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end iff_ops
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