notational update in lambdadelta completed

[helm.git] / matita / matita / contribs / lambdadelta / ground_2 / relocation / nstream_eq.ma

diff --git a/matita/matita/contribs/lambdadelta/ground_2/relocation/nstream_eq.ma b/matita/matita/contribs/lambdadelta/ground_2/relocation/nstream_eq.ma
index cec531469437e7689976f4a209848f8eaa7c81e9..48f3e010042da33afdc150f3137879799ba439de 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/relocation/nstream_eq.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/relocation/nstream_eq.ma
@@ -16,9 +16,9 @@ include "ground_2/relocation/rtmap_eq.ma".
 
 (* RELOCATION N-STREAM ******************************************************)
 
-(* Specific properties on eq ************************************************)
+(* Specific properties ******************************************************)
 
-fact eq_inv_seq_aux: ∀f1,f2,n1,n2. n1@f1 ≗ n2@f2 → n1 = n2 ∧ f1 ≗ f2.
+fact eq_inv_seq_aux: ∀f1,f2,n1,n2. n1⨮f1 ≡ n2⨮f2 → n1 = n2 ∧ f1 ≡ f2.
 #f1 #f2 #n1 #n2 @(nat_elim2 … n1 n2) -n1 -n2
 [ #n2 #H elim (eq_inv_px … H) -H [2,3: // ]
   #g1 #H1 #H elim (push_inv_seq_dx … H) -H /2 width=1 by conj/
@@ -28,11 +28,11 @@ fact eq_inv_seq_aux: ∀f1,f2,n1,n2. n1@f1 ≗ n2@f2 → n1 = n2 ∧ f1 ≗ f2.
 ]
 qed-.
 
-lemma eq_inv_seq: â\88\80g1,g2. g1 â\89\97 g2 â\86\92 â\88\80f1,f2,n1,n2. n1@f1 = g1 â\86\92 n2@f2 = g2 →
-                  n1 = n2 â\88§ f1 â\89\97 f2.
+lemma eq_inv_seq: â\88\80g1,g2. g1 â\89¡ g2 â\86\92 â\88\80f1,f2,n1,n2. n1⨮f1 = g1 â\86\92 n2⨮f2 = g2 →
+                  n1 = n2 â\88§ f1 â\89¡ f2.
 /2 width=1 by eq_inv_seq_aux/ qed-.
 
-let corec nstream_eq: ∀f1,f2. f1 ≗ f2 → f1 ≐ f2 ≝ ?.
+corec lemma nstream_eq: ∀f1,f2. f1 ≡ f2 → f1 ≗ f2.
 * #n1 #f1 * #n2 #f2 #Hf cases (eq_inv_gen … Hf) -Hf *
 #g1 #g2 #Hg #H1 #H2
 [ cases (push_inv_seq_dx … H1) -H1 * -n1 #H1
@@ -45,11 +45,11 @@ let corec nstream_eq: ∀f1,f2. f1 ≗ f2 → f1 ≐ f2 ≝ ?.
 ]
 qed-.
 
-let corec nstream_inv_eq: ∀f1,f2. f1 ≐ f2 → f1 ≗ f2 ≝ ?.
+corec lemma nstream_inv_eq: ∀f1,f2. f1 ≗ f2 → f1 ≡ f2.
 * #n1 #f1 * #n2 #f2 #H cases (eq_stream_inv_seq ??? H) -H [2,3,4,5,6,7: // ]
 #Hf * -n2 cases n1 -n1 /3 width=5 by eq_push/
 #n @eq_next /3 width=5 by eq_seq/
 qed.
 
-lemma eq_seq_id: â\88\80f1,f2. f1 â\89\97 f2 â\86\92 â\88\80n. n@f1 â\89\97 n@f2.
+lemma eq_seq_id: â\88\80f1,f2. f1 â\89¡ f2 â\86\92 â\88\80n. n⨮f1 â\89¡ n⨮f2.
 /4 width=1 by nstream_inv_eq, nstream_eq, eq_seq/ qed.