X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground_2%2Flib%2Fstreams_eq.ma;h=878185ca18e89c24048ea6f0e8ce29fc58ab321b;hb=a77d0bd6a04e94f765d329d47b37d9e04d349b14;hp=839811603e97da52ff2d9fd5b8a138ac62f13303;hpb=859c5cbb8ebffeddd1dd9cbc462e046b0709b4e4;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/ground_2/lib/streams_eq.ma b/matita/matita/contribs/lambdadelta/ground_2/lib/streams_eq.ma
index 839811603..878185ca1 100644
--- a/matita/matita/contribs/lambdadelta/ground_2/lib/streams_eq.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/lib/streams_eq.ma
@@ -12,43 +12,43 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "ground_2/notation/relations/exteq_3.ma".
+include "ground_2/notation/relations/ringeq_3.ma".
 include "ground_2/lib/streams.ma".
 
 (* STREAMS ******************************************************************)
 
 coinductive eq_stream (A): relation (stream A) ≝
-| eq_seq: ∀t1,t2,b1,b2. b1 = b2 → eq_stream A t1 t2 → eq_stream A (b1@t1) (b2@t2)
+| eq_seq: ∀t1,t2,b1,b2. b1 = b2 → eq_stream A t1 t2 → eq_stream A (b1⨮t1) (b2⨮t2)
 .
 
 interpretation "extensional equivalence (nstream)"
-   'ExtEq A t1 t2 = (eq_stream A t1 t2).
+   'RingEq A t1 t2 = (eq_stream A t1 t2).
 
 definition eq_stream_repl (A) (R:relation …) ≝
-                          ∀t1,t2. t1 ≐⦋A⦌ t2 → R t1 t2.
+                          ∀t1,t2. t1 ≗{A} t2 → R t1 t2.
 
 definition eq_stream_repl_back (A) (R:predicate …) ≝
-                               ∀t1. R t1 → ∀t2. t1 ≐⦋A⦌ t2 → R t2.
+                               ∀t1. R t1 → ∀t2. t1 ≗{A} t2 → R t2.
 
 definition eq_stream_repl_fwd (A) (R:predicate …) ≝
-                              ∀t1. R t1 → ∀t2. t2 ≐⦋A⦌ t1 → R t2.
+                              ∀t1. R t1 → ∀t2. t2 ≗{A} t1 → R t2.
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma eq_stream_inv_seq: ∀A,t1,t2. t1 ≐⦋A⦌ t2 →
-                         ∀u1,u2,a1,a2. a1@u1 = t1 → a2@u2 = t2 →
-                         u1 ≐ u2 ∧ a1 = a2.
+lemma eq_stream_inv_seq: ∀A,t1,t2. t1 ≗{A} t2 →
+                         ∀u1,u2,a1,a2. a1⨮u1 = t1 → a2⨮u2 = t2 →
+                         u1 ≗ u2 ∧ a1 = a2.
 #A #t1 #t2 * -t1 -t2
 #t1 #t2 #b1 #b2 #Hb #Ht #u1 #u2 #a1 #a2 #H1 #H2 destruct /2 width=1 by conj/
 qed-.
 
 (* Basic properties *********************************************************)
 
-let corec eq_stream_refl: ∀A. reflexive … (eq_stream A) ≝ ?.
+corec lemma eq_stream_refl: ∀A. reflexive … (eq_stream A).
 #A * #b #t @eq_seq //
 qed.
 
-let corec eq_stream_sym: ∀A. symmetric … (eq_stream A) ≝ ?.
+corec lemma eq_stream_sym: ∀A. symmetric … (eq_stream A).
 #A #t1 #t2 * -t1 -t2
 #t1 #t2 #b1 #b2 #Hb #Ht @eq_seq /2 width=1 by/
 qed-.
@@ -58,14 +58,14 @@ lemma eq_stream_repl_sym: ∀A,R. eq_stream_repl_back A R → eq_stream_repl_fwd
 
 (* Main properties **********************************************************)
 
-let corec eq_stream_trans: ∀A. Transitive … (eq_stream A) ≝ ?.
+corec theorem eq_stream_trans: ∀A. Transitive … (eq_stream A).
 #A #t1 #t * -t1 -t
 #t1 #t #b1 #b * #Ht1 * #b2 #t2 #H cases (eq_stream_inv_seq A … H) -H -b
 /3 width=7 by eq_seq/
 qed-.
 
-theorem eq_stream_canc_sn: ∀A,t,t1,t2. t ≐ t1 → t ≐ t2 → t1 ≐⦋A⦌ t2.
+theorem eq_stream_canc_sn: ∀A,t,t1,t2. t ≗ t1 → t ≗ t2 → t1 ≗{A} t2.
 /3 width=3 by eq_stream_trans, eq_stream_sym/ qed-.
 
-theorem eq_stream_canc_dx: ∀A,t,t1,t2. t1 ≐ t → t2 ≐ t → t1 ≐⦋A⦌ t2.
+theorem eq_stream_canc_dx: ∀A,t,t1,t2. t1 ≗ t → t2 ≗ t → t1 ≗{A} t2.
 /3 width=3 by eq_stream_trans, eq_stream_sym/ qed-.