X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground%2Flib%2Fexteq.ma;h=8c8f218a17c287f6d91d45d0f187cbcb27204262;hb=6f1b6f85a78d4c8da42f035f433fe4b85962bd9b;hp=81c5373a0d9b7ba4ab8559b169e32da074fe7776;hpb=55c768d7e45babb300b5010463ba3196a68f1bbe;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/ground/lib/exteq.ma b/matita/matita/contribs/lambdadelta/ground/lib/exteq.ma
index 81c5373a0..8c8f218a1 100644
--- a/matita/matita/contribs/lambdadelta/ground/lib/exteq.ma
+++ b/matita/matita/contribs/lambdadelta/ground/lib/exteq.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "ground/notation/relations/doteq_4.ma".
+include "ground/notation/relations/circled_eq_4.ma".
 include "ground/lib/relations.ma".
 
 (* EXTENSIONAL EQUIVALENCE FOR FUNCTIONS ************************************)
@@ -22,7 +22,7 @@ definition exteq (A,B:Type[0]): relation (A → B) ≝
 
 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 ******************************************************)
 
@@ -53,27 +53,27 @@ lemma exteq_canc_dx (A) (B):
 (* Constructions with compose ***********************************************)
 
 lemma compose_repl_fwd_dx (A) (B) (C) (g) (f1) (f2):
-      f1 ≐{A,B} f2 → g ∘ f1 ≐{A,C} g ∘ f2.
+      f1 ⊜{A,B} f2 → g ∘ f1 ⊜{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 ≐{A,B} f2 → g ∘ f2 ≐{A,C} g ∘ f1.
+      f1 ⊜{A,B} f2 → g ∘ f2 ⊜{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 ≐{B,C} g2 → g1 ∘ f ≐{A,C} g2 ∘ f.
+      g1 ⊜{B,C} g2 → g1 ∘ f ⊜{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 ≐{B,C} g2 → g2 ∘ f ≐{A,C} g1 ∘ f.
+      g1 ⊜{B,C} g2 → g2 ∘ f ⊜{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 ∘ (f2 ∘ f1) ≐ f3 ∘ f2 ∘ f1.
+      f3 ∘ (f2 ∘ f1) ⊜ f3 ∘ f2 ∘ f1.
 // qed.