feat(library/standard/logic): add identities

library/standard/data/sum.lean

@@ -24,7 +24,7 @@ abbreviation cases_on {A B : Type} {P : (A + B) → Prop} (s : A + B)
 sum_rec H1 H2 s
 
 -- Here is the trick for the theorems that follow:
--- Fixing a1, "f s" is a recursive description of "inl B1 a1 = s".
+-- Fixing a1, "f s" is a recursive description of "inl B a1 = s".
 -- When s is (inl B a1), it reduces to a1 = a1.
 -- When s is (inl B a2), it reduces to a1 = a2.
 -- When s is (inr A b), it reduces to false.

library/standard/logic/connectives/basic.lean

@@ -179,6 +179,7 @@ iff_intro
   (assume Hb, iff_elim_right H Hb)
   (assume Ha, iff_elim_left H Ha)
 
+calc_refl iff_refl
 calc_trans iff_trans
 
 

library/standard/logic/connectives/connectives.md

@@ -10,4 +10,5 @@ Logical operations and connectives.
 * [quantifiers](quantifiers.lean) : existential and universal quantifiers
 * [if](if.lean) : if-then-else
 * [instances](instances.lean) : type class instances
+* [identities](identities.lean) : some useful identities
 * [examples](examples/examples.md)

library/standard/logic/connectives/instances.lean

@@ -119,8 +119,6 @@ theorem subst_iff {P : Prop → Prop} {C : congr iff iff P} {a b : Prop} (H : a
 -- Support for calculations with iff
 -- ----------------
 
-calc_refl iff_refl
-calc_trans iff_trans
 calc_subst subst_iff
 
 namespace iff_ops

library/standard/logic/default.lean

@@ -6,4 +6,4 @@
 
 import logic.connectives.basic logic.connectives.eq logic.connectives.quantifiers
 import logic.classes.decidable logic.classes.inhabited logic.connectives.instances
-import logic.connectives.if
+import logic.connectives.if logic.connectives.identities

library/standard/struc/binary.lean

@@ -1,8 +1,6 @@
-----------------------------------------------------------------------------------------------------
 -- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
 -- Released under Apache 2.0 license as described in the file LICENSE.
 -- Author: Leonardo de Moura
-----------------------------------------------------------------------------------------------------
 
 import logic.connectives.eq
 using eq_ops