update in ground_2, static_2, basic_2, apps_2, alpha_1

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

diff --git a/matita/matita/contribs/lambdadelta/ground_2/relocation/nstream_after.ma b/matita/matita/contribs/lambdadelta/ground_2/relocation/nstream_after.ma
index 6ce6fa476a68bc4e2ed4587653a9f4e0d25b2677..ca3ad7bc7c44535ed250d434ea40d6549336f835 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/relocation/nstream_after.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/relocation/nstream_after.ma
@@ -18,7 +18,7 @@ include "ground_2/relocation/rtmap_after.ma".
 (* RELOCATION N-STREAM ******************************************************)
 
 corec definition compose: rtmap → rtmap → rtmap.
-#f2 * #n1 #f1 @(seq â\80¦ (f2@â\9d´n1â\9dµ)) @(compose ? f1) -compose -f1
+#f2 * #n1 #f1 @(seq â\80¦ (f2@â\9d¨n1â\9d©)) @(compose ? f1) -compose -f1
 @(⫰*[↑n1] f2)
 defined.
 
@@ -27,7 +27,7 @@ interpretation "functional composition (nstream)"
 
 (* Basic properies on compose ***********************************************)
 
-lemma compose_rew: â\88\80f2,f1,n1. f2@â\9d´n1â\9dµ⨮(⫰*[↑n1]f2)∘f1 = f2∘(n1⨮f1).
+lemma compose_rew: â\88\80f2,f1,n1. f2@â\9d¨n1â\9d©⨮(⫰*[↑n1]f2)∘f1 = f2∘(n1⨮f1).
 #f2 #f1 #n1 <(stream_rew … (f2∘(n1⨮f1))) normalize //
 qed.
 
@@ -39,7 +39,7 @@ qed.
 (* Basic inversion lemmas on compose ****************************************)
 
 lemma compose_inv_rew: ∀f2,f1,f,n1,n. f2∘(n1⨮f1) = n⨮f →
-                       f2@â\9d´n1â\9dµ = n ∧ (⫰*[↑n1]f2)∘f1 = f.
+                       f2@â\9d¨n1â\9d© = n ∧ (⫰*[↑n1]f2)∘f1 = f.
 #f2 #f1 #f #n1 #n <(stream_rew … (f2∘(n1⨮f1))) normalize
 #H destruct /2 width=1 by conj/
 qed-.
@@ -51,13 +51,13 @@ lemma compose_inv_O2: ∀f2,f1,f,n2,n. (n2⨮f2)∘(⫯f1) = n⨮f →
 qed-.
 
 lemma compose_inv_S2: ∀f2,f1,f,n2,n1,n. (n2⨮f2)∘(↑n1⨮f1) = n⨮f →
-                      â\86\91(n2+f2@â\9d´n1â\9dµ) = n â\88§ f2â\88\98(n1⨮f1) = f2@â\9d´n1â\9dµ⨮f.
+                      â\86\91(n2+f2@â\9d¨n1â\9d©) = n â\88§ f2â\88\98(n1⨮f1) = f2@â\9d¨n1â\9d©⨮f.
 #f2 #f1 #f #n2 #n1 #n <compose_rew
 #H destruct <tls_S1 /2 width=1 by conj/
 qed-.
 
 lemma compose_inv_S1: ∀f2,f1,f,n1,n. (↑f2)∘(n1⨮f1) = n⨮f →
-                      â\86\91(f2@â\9d´n1â\9dµ) = n â\88§ f2â\88\98(n1⨮f1) = f2@â\9d´n1â\9dµ⨮f.
+                      â\86\91(f2@â\9d¨n1â\9d©) = n â\88§ f2â\88\98(n1⨮f1) = f2@â\9d¨n1â\9d©⨮f.
 #f2 #f1 #f #n1 #n <compose_rew
 #H destruct <tls_S1 /2 width=1 by conj/
 qed-.
@@ -74,7 +74,7 @@ lemma after_S2: ∀f2,f1,f,n1,n. f2 ⊚ n1⨮f1 ≘ n⨮f →
 #f2 #f1 #f #n1 #n #Hf #n2 elim n2 -n2 /2 width=7 by after_next, after_push/
 qed.
 
-lemma after_apply: â\88\80n1,f2,f1,f. (â«°*[â\86\91n1] f2) â\8a\9a f1 â\89\98 f â\86\92 f2 â\8a\9a n1⨮f1 â\89\98 f2@â\9d´n1â\9dµ⨮f.
+lemma after_apply: â\88\80n1,f2,f1,f. (â«°*[â\86\91n1] f2) â\8a\9a f1 â\89\98 f â\86\92 f2 â\8a\9a n1⨮f1 â\89\98 f2@â\9d¨n1â\9d©⨮f.
 #n1 elim n1 -n1
 [ * /2 width=1 by after_O2/
 | #n1 #IH * /3 width=1 by after_S2/
@@ -134,7 +134,7 @@ lemma after_inv_total: ∀f2,f1,f. f2 ⊚ f1 ≘ f → f2 ∘ f1 ≡ f.
 
 (* Specific forward lemmas on after *****************************************)
 
-lemma after_fwd_hd: â\88\80f2,f1,f,n1,n. f2 â\8a\9a n1⨮f1 â\89\98 n⨮f â\86\92 f2@â\9d´n1â\9dµ = n.
+lemma after_fwd_hd: â\88\80f2,f1,f,n1,n. f2 â\8a\9a n1⨮f1 â\89\98 n⨮f â\86\92 f2@â\9d¨n1â\9d© = n.
 #f2 #f1 #f #n1 #n #H lapply (after_fwd_at ? n1 0 … H) -H [1,2,3: // ]
 /3 width=2 by at_inv_O1, sym_eq/
 qed-.
@@ -149,10 +149,10 @@ lemma after_fwd_tls: ∀f,f1,n1,f2,n2,n. n2⨮f2 ⊚ n1⨮f1 ≘ n⨮f →
 qed-.
 
 lemma after_inv_apply: ∀f2,f1,f,n2,n1,n. n2⨮f2 ⊚ n1⨮f1 ≘ n⨮f →
-                       (n2⨮f2)@â\9d´n1â\9dµ = n ∧ (⫰*[n1]f2) ⊚ f1 ≘ f.
+                       (n2⨮f2)@â\9d¨n1â\9d© = n ∧ (⫰*[n1]f2) ⊚ f1 ≘ f.
 /3 width=3 by after_fwd_tls, after_fwd_hd, conj/ qed-.
 
 (* Properties on apply ******************************************************)
 
-lemma compose_apply (f2) (f1) (i): f2@â\9d´f1@â\9d´iâ\9dµâ\9dµ = (f2â\88\98f1)@â\9d´iâ\9dµ.
+lemma compose_apply (f2) (f1) (i): f2@â\9d¨f1@â\9d¨iâ\9d©â\9d© = (f2â\88\98f1)@â\9d¨iâ\9d©.
 /4 width=6 by after_fwd_at, at_inv_total, sym_eq/ qed.