update in ground

[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..81c5373a0d9b7ba4ab8559b169e32da074fe7776 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground/lib/exteq.ma
+++ b/matita/matita/contribs/lambdadelta/ground/lib/exteq.ma
@@ -15,7 +15,7 @@
 include "ground/notation/relations/doteq_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.
@@ -26,25 +26,31 @@ interpretation
 
 (* 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 ≐{A,B} f2 → g ∘ f1 ≐{A,C} g ∘ f2.