update in ground, static_2 and apps_2

[helm.git] / matita / matita / contribs / lambdadelta / ground / lib / exteq.ma

diff --git a/matita/matita/contribs/lambdadelta/ground/lib/exteq.ma b/matita/matita/contribs/lambdadelta/ground/lib/exteq.ma
index 5b655e686a5cec35230bedbe9bc819e9d717ed6e..8c8f218a17c287f6d91d45d0f187cbcb27204262 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground/lib/exteq.ma
+++ b/matita/matita/contribs/lambdadelta/ground/lib/exteq.ma
@@ -12,62 +12,68 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "ground/notation/relations/doteq_4.ma".
+include "ground/notation/relations/circled_eq_4.ma".
 include "ground/lib/relations.ma".
 
-(* EXTENSIONAL EQUIVALENCE **************************************************)
+(* EXTENSIONAL EQUIVALENCE FOR FUNCTIONS ************************************)
 
 definition exteq (A,B:Type[0]): relation (A → B) ≝
            λf1,f2. ∀a. f1 a = f2 a.
 
 interpretation
   "extensional equivalence"
-  'DotEq A B f1 f2 = (exteq A B f1 f2).
+  'CircledEq A B f1 f2 = (exteq A B f1 f2).
 
 (* Basic constructions ******************************************************)
 
-lemma exteq_refl (A) (B): reflexive … (exteq A B).
+lemma exteq_refl (A) (B):
+      reflexive … (exteq A B).
 // qed.
 
-lemma exteq_repl (A) (B): replace_2 … (exteq A B) (exteq A B) (exteq A B).
+lemma exteq_repl (A) (B):
+      replace_2 … (exteq A B) (exteq A B) (exteq A B).
 // qed-.
 
-lemma exteq_sym (A) (B): symmetric … (exteq A B).
+lemma exteq_sym (A) (B):
+      symmetric … (exteq A B).
 /2 width=1 by exteq_repl/ qed-.
 
-lemma exteq_trans (A) (B): Transitive … (exteq A B).
+lemma exteq_trans (A) (B):
+      Transitive … (exteq A B).
 /2 width=1 by exteq_repl/ qed-.
 
-lemma exteq_canc_sn (A) (B): left_cancellable … (exteq A B).
+lemma exteq_canc_sn (A) (B):
+      left_cancellable … (exteq A B).
 /2 width=1 by exteq_repl/ qed-.
 
-lemma exteq_canc_dx (A) (B): right_cancellable … (exteq A B).
+lemma exteq_canc_dx (A) (B):
+      right_cancellable … (exteq A B).
 /2 width=1 by exteq_repl/ qed-.
 
-(* Constructions with function composition **********************************)
+(* Constructions with compose ***********************************************)
 
 lemma compose_repl_fwd_dx (A) (B) (C) (g) (f1) (f2):
-      f1 â\89\90{A,B} f2 â\86\92 g â\88\98 f1 â\89\90{A,C} g ∘ f2.
+      f1 â\8a\9c{A,B} f2 â\86\92 g â\88\98 f1 â\8a\9c{A,C} g ∘ f2.
 #A #B #C #g #f1 #f2 #Hf12 #a
 whd in ⊢ (??%%); //
 qed.
 
 lemma compose_repl_bak_dx (A) (B) (C) (g) (f1) (f2):
-      f1 â\89\90{A,B} f2 â\86\92 g â\88\98 f2 â\89\90{A,C} g ∘ f1.
+      f1 â\8a\9c{A,B} f2 â\86\92 g â\88\98 f2 â\8a\9c{A,C} g ∘ f1.
 /3 width=1 by compose_repl_fwd_dx, exteq_sym/
 qed.
 
 lemma compose_repl_fwd_sn (A) (B) (C) (g1) (g2) (f):
-      g1 â\89\90{B,C} g2 â\86\92 g1 â\88\98 f â\89\90{A,C} g2 ∘ f.
+      g1 â\8a\9c{B,C} g2 â\86\92 g1 â\88\98 f â\8a\9c{A,C} g2 ∘ f.
 #A #B #C #g1 #g2 #f #Hg12 #a
 whd in ⊢ (??%%); //
 qed.
 
 lemma compose_repl_bak_sn (A) (B) (C) (g1) (g2) (f):
-      g1 â\89\90{B,C} g2 â\86\92 g2 â\88\98 f â\89\90{A,C} g1 ∘ f.
+      g1 â\8a\9c{B,C} g2 â\86\92 g2 â\88\98 f â\8a\9c{A,C} g1 ∘ f.
 /3 width=1 by compose_repl_fwd_sn, exteq_sym/
 qed.
 
 lemma compose_assoc (A1) (A2) (A3) (A4) (f3:A3→A4) (f2:A2→A3) (f1:A1→A2):
-      f3 â\88\98 (f2 â\88\98 f1) â\89\90 f3 ∘ f2 ∘ f1.
+      f3 â\88\98 (f2 â\88\98 f1) â\8a\9c f3 ∘ f2 ∘ f1.
 // qed.