X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fs_computation%2Ffqus.ma;h=32555f1f6d3ab551bc8669dafc82490d56e5ab16;hp=40d4124a5acacd521a3be96c8aea2740b8df950a;hb=222044da28742b24584549ba86b1805a87def070;hpb=75f395f0febd02de8e0f881d918a8812b1425c8d

diff --git a/matita/matita/contribs/lambdadelta/basic_2/s_computation/fqus.ma b/matita/matita/contribs/lambdadelta/basic_2/s_computation/fqus.ma
index 40d4124a5..32555f1f6 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/s_computation/fqus.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/s_computation/fqus.ma
@@ -30,17 +30,17 @@ interpretation "star-iterated structural successor (closure)"
 
 (* Basic eliminators ********************************************************)
 
-lemma fqus_ind: ∀b,G1,L1,T1. ∀R:relation3 …. R G1 L1 T1 →
-                (∀G,G2,L,L2,T,T2. ⦃G1, L1, T1⦄ ⊐*[b] ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊐⸮[b] ⦃G2, L2, T2⦄ → R G L T → R G2 L2 T2) →
-                ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐*[b] ⦃G2, L2, T2⦄ → R G2 L2 T2.
+lemma fqus_ind: ∀b,G1,L1,T1. ∀Q:relation3 …. Q G1 L1 T1 →
+                (∀G,G2,L,L2,T,T2. ⦃G1, L1, T1⦄ ⊐*[b] ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊐⸮[b] ⦃G2, L2, T2⦄ → Q G L T → Q G2 L2 T2) →
+                ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐*[b] ⦃G2, L2, T2⦄ → Q G2 L2 T2.
 #b #G1 #L1 #T1 #R #IH1 #IH2 #G2 #L2 #T2 #H
 @(tri_TC_star_ind … IH1 IH2 G2 L2 T2 H) //
 qed-.
 
-lemma fqus_ind_dx: ∀b,G2,L2,T2. ∀R:relation3 …. R G2 L2 T2 →
-                   (∀G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ⊐⸮[b] ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊐*[b] ⦃G2, L2, T2⦄ → R G L T → R G1 L1 T1) →
-                   ∀G1,L1,T1. ⦃G1, L1, T1⦄ ⊐*[b] ⦃G2, L2, T2⦄ → R G1 L1 T1.
-#b #G2 #L2 #T2 #R #IH1 #IH2 #G1 #L1 #T1 #H
+lemma fqus_ind_dx: ∀b,G2,L2,T2. ∀Q:relation3 …. Q G2 L2 T2 →
+                   (∀G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ⊐⸮[b] ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊐*[b] ⦃G2, L2, T2⦄ → Q G L T → Q G1 L1 T1) →
+                   ∀G1,L1,T1. ⦃G1, L1, T1⦄ ⊐*[b] ⦃G2, L2, T2⦄ → Q G1 L1 T1.
+#b #G2 #L2 #T2 #Q #IH1 #IH2 #G1 #L1 #T1 #H
 @(tri_TC_star_ind_dx … IH1 IH2 G1 L1 T1 H) //
 qed-.
 
@@ -81,7 +81,7 @@ qed-.
 lemma fqus_inv_lref1: ∀b,G1,G2,L1,L2,T2,i. ⦃G1, L1, #i⦄ ⊐*[b] ⦃G2, L2, T2⦄ →
                       ∨∨ ∧∧ G1 = G2 & L1 = L2 & #i = T2
                        | ∃∃J,L,V. ⦃G1, L, V⦄ ⊐*[b] ⦃G2, L2, T2⦄ & L1 = L.ⓑ{J}V & i = 0
-                       | ∃∃J,L,j. ⦃G1, L, #j⦄ ⊐*[b] ⦃G2, L2, T2⦄ & L1 = L.ⓘ{J} & i = ⫯j.
+                       | ∃∃J,L,j. ⦃G1, L, #j⦄ ⊐*[b] ⦃G2, L2, T2⦄ & L1 = L.ⓘ{J} & i = ↑j.
 #b #G1 #G2 #L1 #L2 #T2 #i #H elim (fqus_inv_fqu_sn … H) -H * /3 width=1 by and3_intro, or3_intro0/
 #G #L #T #H elim (fqu_inv_lref1 … H) -H * /3 width=7 by or3_intro1, or3_intro2, ex3_4_intro, ex3_3_intro/
 qed-.
@@ -149,8 +149,8 @@ lemma fqus_inv_zero1_pair: ∀b,I,G1,G2,L1,L2,V1,T2. ⦃G1, L1.ⓑ{I}V1, #0⦄ 
 #H1 #H2 #H3 #H destruct /2 width=1 by or_intror/
 qed-.
 
-lemma fqus_inv_lref1_bind: ∀b,I,G1,G2,L1,L2,T2,i. ⦃G1, L1.ⓘ{I}, #⫯i⦄ ⊐*[b] ⦃G2, L2, T2⦄ →
-                           (∧∧ G1 = G2 & L1.ⓘ{I} = L2 & #(⫯i) = T2) ∨ ⦃G1, L1, #i⦄ ⊐*[b] ⦃G2, L2, T2⦄.
+lemma fqus_inv_lref1_bind: ∀b,I,G1,G2,L1,L2,T2,i. ⦃G1, L1.ⓘ{I}, #↑i⦄ ⊐*[b] ⦃G2, L2, T2⦄ →
+                           (∧∧ G1 = G2 & L1.ⓘ{I} = L2 & #(↑i) = T2) ∨ ⦃G1, L1, #i⦄ ⊐*[b] ⦃G2, L2, T2⦄.
 #b #I #G1 #G2 #L1 #L2 #T2 #i #H elim (fqus_inv_fqu_sn … H) -H * /3 width=1 by and3_intro, or_introl/
 #G #L #T #H elim (fqu_inv_lref1_bind … H) -H
 #H1 #H2 #H3 #H destruct /2 width=1 by or_intror/