update in basic_2 and ground_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve_far.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve_far.ma
index 971541b21fe05ce14b2b42f6f4a32c379444e8ac..7ab0ff8a2b309828cf94be53859587cbe8565ecc 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve_far.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve_far.ma
@@ -12,75 +12,22 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/predstar_7.ma".
-include "basic_2/rt_computation/fpbg.ma".
-include "basic_2/rt_computation/cpms_fpbs.ma".
-include "basic_2/dynamic/cnv.ma".
+include "basic_2/dynamic/cnv_cpm_trans.ma".
 
 (* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
 
-(* Inductive premises for the preservation results **************************)
+(* Far properties for preservation ******************************************)
 
-definition cpsms (n) (h) (o): relation4 genv lenv term term ≝ λG,L,T1,T2.
-                 ∃∃n1,n2,T. T1 ≛[h,o] T → ⊥ & ⦃G, L⦄ ⊢ T1 ➡[n1,h] T & ⦃G, L⦄ ⊢ T ➡*[n2,h] T2 & n1+n2 = n.
-
-interpretation
-   "context-sensitive parallel stratified t-bound  rt-computarion (term)"
-   'PRedStar n h o G L T1 T2 = (cpsms n h o G L T1 T2).
-
-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_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_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_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_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_cpsms_conf_lpr (a) (h) (o): relation3 genv lenv term ≝
-                                 λG,L0,T0. ⦃G, L0⦄ ⊢ T0 ![a,h] →
-                                 ∀n1,T1. ⦃G, L0⦄ ⊢ T0 ➡*[n1,h,o] T1 → ∀n2,T2. ⦃G, L0⦄ ⊢ T0 ➡*[n2,h,o] 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.
-
-(* Properties for preservation **********************************************)
-
-lemma cnv_cpms_trans_lpr_far (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_far (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_trans_lpr a h G1 L1 T1) →
+                            ∀G1,L1,T1. G0 = G1 → L0 = L1 → T0 = T1 → IH_cnv_cpms_trans_lpr a h G1 L1 T1.
+#a #h #o #G0 #L0 #T0 #IH2 #IH1 #G1 #L1 #T1 #HG #HL #HT #H0 #n #T2 #H destruct
 @(cpms_ind_dx … H) -n -T2
-/4 width=7 by cpms_fwd_fpbs, fpbg_fpbs_trans/
+[ #L2 #HL12 @(cnv_cpm_trans_lpr_aux … IH2 IH1 … H0 … 0 T1 … HL12) -L2 -IH2 -IH1 -H0 //
+| #n2 #n2 #T #T2 #HT1 #IH #HT2 #L2 #HL12 destruct
+  @(cnv_cpm_trans_lpr_aux … o … HT2 … HL12) [1,2,3,6,7,8,9: /2 width=2 by/ ] -n2 -L2 -T2 -IH
+  /3 width=4 by cpms_fpbg_trans/
+]
 qed-.
-
-lemma cnv_cpm_conf_lpr_far (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.
-/3 width=8 by cpm_cpms/ qed-.
-
-lemma cnv_cpms_strip_lpr_far (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.
-/3 width=8 by cpm_cpms/ qed-.