Merge branch 'matita-lablgtk3' of ssh://matita.cs.unibo.it:/srv/git/helm into matita...

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve_sub.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve_sub.ma
index c99d6a5c08a7387f6416eee775775f3b520f73fd..94037ce79cd9628a784dd7cfea6e9015bdf0a048 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve_sub.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve_sub.ma
@@ -19,53 +19,53 @@ include "basic_2/dynamic/cnv.ma".
 
 (* Inductive premises for the preservation results **************************)
 
-definition IH_cnv_cpm_trans_lpr (a) (h): relation3 genv lenv term ≝
-                                λG,L1,T1. ⦃G, L1⦄ ⊢ T1 ![a,h] →
-                                ∀n,T2. ⦃G, L1⦄ ⊢ T1 ➡[n,h] T2 →
-                                ∀L2. ⦃G, L1⦄ ⊢ ➡[h] L2 → ⦃G, L2⦄ ⊢ T2 ![a,h].
+definition IH_cnv_cpm_trans_lpr (h) (a): relation3 genv lenv term ≝
+                                λG,L1,T1. ⦃G,L1⦄ ⊢ T1 ![h,a] →
+                                ∀n,T2. ⦃G,L1⦄ ⊢ T1 ➡[n,h] T2 →
+                                ∀L2. ⦃G,L1⦄ ⊢ ➡[h] L2 → ⦃G,L2⦄ ⊢ T2 ![h,a].
 
-definition IH_cnv_cpms_trans_lpr (a) (h): relation3 genv lenv term ≝
-                                 λG,L1,T1. ⦃G, L1⦄ ⊢ T1 ![a,h] →
-                                 ∀n,T2. ⦃G, L1⦄ ⊢ T1 ➡*[n,h] T2 →
-                                 ∀L2. ⦃G, L1⦄ ⊢ ➡[h] L2 → ⦃G, L2⦄ ⊢ T2 ![a,h].
+definition IH_cnv_cpms_trans_lpr (h) (a): relation3 genv lenv term ≝
+                                 λG,L1,T1. ⦃G,L1⦄ ⊢ T1 ![h,a] →
+                                 ∀n,T2. ⦃G,L1⦄ ⊢ T1 ➡*[n,h] T2 →
+                                 ∀L2. ⦃G,L1⦄ ⊢ ➡[h] L2 → ⦃G,L2⦄ ⊢ T2 ![h,a].
 
-definition IH_cnv_cpm_conf_lpr (a) (h): relation3 genv lenv term ≝
-                               λG,L0,T0. ⦃G, L0⦄ ⊢ T0 ![a,h] →
-                               ∀n1,T1. ⦃G, L0⦄ ⊢ T0 ➡[n1,h] T1 → ∀n2,T2. ⦃G, L0⦄ ⊢ T0 ➡[n2,h] T2 →
-                               ∀L1. ⦃G, L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G, L0⦄ ⊢ ➡[h] L2 →
-                               ∃∃T. ⦃G, L1⦄ ⊢ T1 ➡*[n2-n1,h] T & ⦃G, L2⦄ ⊢ T2 ➡*[n1-n2,h] T.
+definition IH_cnv_cpm_conf_lpr (h) (a): relation3 genv lenv term ≝
+                               λG,L0,T0. ⦃G,L0⦄ ⊢ T0 ![h,a] →
+                               ∀n1,T1. ⦃G,L0⦄ ⊢ T0 ➡[n1,h] T1 → ∀n2,T2. ⦃G,L0⦄ ⊢ T0 ➡[n2,h] T2 →
+                               ∀L1. ⦃G,L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G,L0⦄ ⊢ ➡[h] L2 →
+                               ∃∃T. ⦃G,L1⦄ ⊢ T1 ➡*[n2-n1,h] T & ⦃G,L2⦄ ⊢ T2 ➡*[n1-n2,h] T.
 
-definition IH_cnv_cpms_strip_lpr (a) (h): relation3 genv lenv term ≝
-                                 λG,L0,T0. ⦃G, L0⦄ ⊢ T0 ![a,h] →
-                                 ∀n1,T1. ⦃G, L0⦄ ⊢ T0 ➡*[n1,h] T1 → ∀n2,T2. ⦃G, L0⦄ ⊢ T0 ➡[n2,h] T2 →
-                                 ∀L1. ⦃G, L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G, L0⦄ ⊢ ➡[h] L2 →
-                                 ∃∃T. ⦃G, L1⦄ ⊢ T1 ➡*[n2-n1,h] T & ⦃G, L2⦄ ⊢ T2 ➡*[n1-n2,h] T.
+definition IH_cnv_cpms_strip_lpr (h) (a): relation3 genv lenv term ≝
+                                 λG,L0,T0. ⦃G,L0⦄ ⊢ T0 ![h,a] →
+                                 ∀n1,T1. ⦃G,L0⦄ ⊢ T0 ➡*[n1,h] T1 → ∀n2,T2. ⦃G,L0⦄ ⊢ T0 ➡[n2,h] T2 →
+                                 ∀L1. ⦃G,L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G,L0⦄ ⊢ ➡[h] L2 →
+                                 ∃∃T. ⦃G,L1⦄ ⊢ T1 ➡*[n2-n1,h] T & ⦃G,L2⦄ ⊢ T2 ➡*[n1-n2,h] T.
 
-definition IH_cnv_cpms_conf_lpr (a) (h): relation3 genv lenv term ≝
-                                λG,L0,T0. ⦃G, L0⦄ ⊢ T0 ![a,h] →
-                                ∀n1,T1. ⦃G, L0⦄ ⊢ T0 ➡*[n1,h] T1 → ∀n2,T2. ⦃G, L0⦄ ⊢ T0 ➡*[n2,h] T2 →
-                                ∀L1. ⦃G, L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G, L0⦄ ⊢ ➡[h] L2 →
-                                ∃∃T. ⦃G, L1⦄ ⊢ T1 ➡*[n2-n1,h] T & ⦃G, L2⦄ ⊢ T2 ➡*[n1-n2,h] T.
+definition IH_cnv_cpms_conf_lpr (h) (a): relation3 genv lenv term ≝
+                                λG,L0,T0. ⦃G,L0⦄ ⊢ T0 ![h,a] →
+                                ∀n1,T1. ⦃G,L0⦄ ⊢ T0 ➡*[n1,h] T1 → ∀n2,T2. ⦃G,L0⦄ ⊢ T0 ➡*[n2,h] T2 →
+                                ∀L1. ⦃G,L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G,L0⦄ ⊢ ➡[h] L2 →
+                                ∃∃T. ⦃G,L1⦄ ⊢ T1 ➡*[n2-n1,h] T & ⦃G,L2⦄ ⊢ T2 ➡*[n1-n2,h] T.
 
 (* Auxiliary properties for preservation ************************************)
 
-fact cnv_cpms_trans_lpr_sub (a) (h) (o):
-                            ∀G0,L0,T0.
-                            (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpm_trans_lpr a h G1 L1 T1) →
-                            ∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpms_trans_lpr a h G1 L1 T1.
-#a #h #o #G0 #L0 #T0 #IH #G1 #L1 #T1 #H01 #HT1 #n #T2 #H
+fact cnv_cpms_trans_lpr_sub (h) (a):
+     ∀G0,L0,T0.
+     (∀G1,L1,T1. ⦃G0,L0,T0⦄ >[h] ⦃G1,L1,T1⦄ → IH_cnv_cpm_trans_lpr h a G1 L1 T1) →
+     ∀G1,L1,T1. ⦃G0,L0,T0⦄ >[h] ⦃G1,L1,T1⦄ → IH_cnv_cpms_trans_lpr h a G1 L1 T1.
+#h #a #G0 #L0 #T0 #IH #G1 #L1 #T1 #H01 #HT1 #n #T2 #H
 @(cpms_ind_dx … H) -n -T2
 /3 width=7 by fpbg_cpms_trans/
 qed-.
 
-fact cnv_cpm_conf_lpr_sub (a) (h) (o):
-                          ∀G0,L0,T0.
-                          (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpms_conf_lpr a h G1 L1 T1) →
-                          ∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpm_conf_lpr a h G1 L1 T1.
+fact cnv_cpm_conf_lpr_sub (h) (a):
+     ∀G0,L0,T0.
+     (∀G1,L1,T1. ⦃G0,L0,T0⦄ >[h] ⦃G1,L1,T1⦄ → IH_cnv_cpms_conf_lpr h a G1 L1 T1) →
+     ∀G1,L1,T1. ⦃G0,L0,T0⦄ >[h] ⦃G1,L1,T1⦄ → IH_cnv_cpm_conf_lpr h a G1 L1 T1.
 /3 width=8 by cpm_cpms/ qed-.
 
-fact cnv_cpms_strip_lpr_sub (a) (h) (o):
-                            ∀G0,L0,T0.
-                            (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpms_conf_lpr a h G1 L1 T1) →
-                            ∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpms_strip_lpr a h G1 L1 T1.
+fact cnv_cpms_strip_lpr_sub (h) (a):
+     ∀G0,L0,T0.
+     (∀G1,L1,T1. ⦃G0,L0,T0⦄ >[h] ⦃G1,L1,T1⦄ → IH_cnv_cpms_conf_lpr h a G1 L1 T1) →
+     ∀G1,L1,T1. ⦃G0,L0,T0⦄ >[h] ⦃G1,L1,T1⦄ → IH_cnv_cpms_strip_lpr h a G1 L1 T1.
 /3 width=8 by cpm_cpms/ qed-.