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refactor(library/standard): define abbreviations using '@'

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Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This commit is contained in:
Leonardo de Moura 2014-08-21 18:39:38 -07:00
parent 07bc0727e2
commit c4cc837e34
2 changed files with 14 additions and 14 deletions
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10
library/standard/logic/connectives/basic.lean
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@ -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)

18
library/standard/logic/connectives/instances.lean
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@ -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