milestone in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / dynamic / cnv_cpm_tdeq_trans.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpm_tdeq_trans.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpm_tdeq_trans.ma
index 7b19372587bad0a094c758e0ffe8a67577bd0868..3a3919fc4bddc06454c5c8b44ce1197ffb04b94d 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpm_tdeq_trans.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpm_tdeq_trans.ma
@@ -17,25 +17,25 @@ include "basic_2/dynamic/cnv_cpm_tdeq.ma".
 
 (* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
 
-definition IH_cnv_cpm_tdeq_cpm_trans (a) (h) (o): relation3 genv lenv term ≝
+definition IH_cnv_cpm_tdeq_cpm_trans (a) (h): relation3 genv lenv term ≝
            λG,L,T1. ⦃G, L⦄ ⊢ T1 ![a,h] →
-           ∀n1,T.  ⦃G,L⦄ ⊢ T1 ➡[n1,h] T → T1 ≛[h,o] T →
+           ∀n1,T.  ⦃G,L⦄ ⊢ T1 ➡[n1,h] T → T1 ≛ T →
            ∀n2,T2. ⦃G,L⦄ ⊢ T ➡[n2,h] T2 →
-           ∃∃T0. ⦃G,L⦄ ⊢ T1 ➡[n2,h] T0 & ⦃G,L⦄ ⊢ T0 ➡[n1,h] T2 & T0 ≛[h,o] T2.
+           ∃∃T0. ⦃G,L⦄ ⊢ T1 ➡[n2,h] T0 & ⦃G,L⦄ ⊢ T0 ➡[n1,h] T2 & T0 ≛ T2.
 
 (* Transitive properties restricted rt-transition for terms *****************)
 
-fact cnv_cpm_tdeq_cpm_trans_sub (a) (h) (o) (G0) (L0) (T0):
-     (∀G,L,T. ⦃G0, L0, T0⦄ >[h,o] ⦃G, L, T⦄ → IH_cnv_cpm_trans_lpr a h G L T) →
-     (∀G,L,T. ⦃G0,L0,T0⦄ ⊐+ ⦃G,L,T⦄ → IH_cnv_cpm_tdeq_cpm_trans a h o G L T) →
-     ∀G,L,T1. G0 = G → L0 = L → T0 = T1 → IH_cnv_cpm_tdeq_cpm_trans a h o G L T1.
-#a #h #o #G0 #L0 #T0 #IH2 #IH1 #G #L * [| * [| * ]]
+fact cnv_cpm_tdeq_cpm_trans_sub (a) (h) (G0) (L0) (T0):
+     (∀G,L,T. ⦃G0, L0, T0⦄ >[h] ⦃G, L, T⦄ → IH_cnv_cpm_trans_lpr a h G L T) →
+     (∀G,L,T. ⦃G0,L0,T0⦄ ⊐+ ⦃G,L,T⦄ → IH_cnv_cpm_tdeq_cpm_trans a h G L T) →
+     ∀G,L,T1. G0 = G → L0 = L → T0 = T1 → IH_cnv_cpm_tdeq_cpm_trans a h G L T1.
+#a #h #G0 #L0 #T0 #IH2 #IH1 #G #L * [| * [| * ]]
 [ #I #_ #_ #_ #_ #n1 #X1 #H1X #H2X #n2 #X2 #HX2 destruct -G0 -L0 -T0
   elim (cpm_tdeq_inv_atom_sn … H1X H2X) -H1X -H2X *
   [ #H1 #H2 destruct /2 width=4 by ex3_intro/
-  | #s #H1 #H2 #H3 #Hs destruct
+  | #s #H1 #H2 #H3 destruct
     elim (cpm_inv_sort1 … HX2) -HX2 #H #Hn2 destruct >iter_n_Sm
-    /5 width=6 by cpm_sort, tdeq_sort, deg_iter, deg_next, ex3_intro/
+    /3 width=4 by cpm_sort, tdeq_sort, ex3_intro/
   ]
 | #p #I #V1 #T1 #HG #HL #HT #H0 #n1 #X1 #H1X #H2X #n2 #X2 #HX2 destruct
   elim (cpm_tdeq_inv_bind_sn … H0 … H1X H2X) -H0 -H1X -H2X #T #_ #H0T1 #H1T1 #H2T1 #H destruct
@@ -88,10 +88,10 @@ fact cnv_cpm_tdeq_cpm_trans_sub (a) (h) (o) (G0) (L0) (T0):
 ]
 qed-.
 
-fact cnv_cpm_tdeq_cpm_trans_aux (a) (h) (o) (G0) (L0) (T0):
-     (∀G,L,T. ⦃G0, L0, T0⦄ >[h, o] ⦃G, L, T⦄ → IH_cnv_cpm_trans_lpr a h G L T) →
-     IH_cnv_cpm_tdeq_cpm_trans a h o G0 L0 T0.
-#a #h #o #G0 #L0 #T0
+fact cnv_cpm_tdeq_cpm_trans_aux (a) (h) (G0) (L0) (T0):
+     (∀G,L,T. ⦃G0, L0, T0⦄ >[h] ⦃G, L, T⦄ → IH_cnv_cpm_trans_lpr a h G L T) →
+     IH_cnv_cpm_tdeq_cpm_trans a h G0 L0 T0.
+#a #h #G0 #L0 #T0
 @(fqup_wf_ind (Ⓣ) … G0 L0 T0) -G0 -L0 -T0 #G0 #L0 #T0 #IH #IH0
 /5 width=10 by cnv_cpm_tdeq_cpm_trans_sub, fqup_fpbg_trans/
 qed-.