update in ground_2, static_2, basic_2, apps_2, alpha_1

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve.ma
index 9e93c859d4c096bbedda88d2c206f69bdfb3e096..a7027e195ec234695a8765ea597b271c1946adaf 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve.ma
@@ -19,42 +19,57 @@ include "basic_2/dynamic/cnv_cpms_conf.ma".
 (* Main preservation properties *********************************************)
 
 (* Basic_2A1: uses: snv_preserve *)
-lemma cnv_preserve (a) (h): ∀G,L,T. ⦃G,L⦄ ⊢ T ![a,h] →
-                            ∧∧ IH_cnv_cpms_conf_lpr a h G L T
-                             & IH_cnv_cpm_trans_lpr a h G L T.
-#a #h #G #L #T #HT
-letin o ≝ (sd_O h)
-lapply (cnv_fwd_fsb … o … HT) -HT #H
+lemma cnv_preserve (h) (a): ∀G,L,T. ❪G,L❫ ⊢ T ![h,a] →
+      ∧∧ IH_cnv_cpms_conf_lpr h a G L T
+       & IH_cnv_cpm_trans_lpr h a G L T.
+#h #a #G #L #T #HT
+lapply (cnv_fwd_fsb … HT) -HT #H
 @(fsb_ind_fpbg … H) -G -L -T #G #L #T #_ #IH
 @conj [ letin aux ≝ cnv_cpms_conf_lpr_aux | letin aux ≝ cnv_cpm_trans_lpr_aux ]
-@(aux … o … G L T) // #G0 #L0 #T0 #H
+@(aux … G L T) // #G0 #L0 #T0 #H
 elim (IH … H) -IH -H //
 qed-.
 
-theorem cnv_cpms_conf_lpr (a) (h) (G) (L) (T): IH_cnv_cpms_conf_lpr a h G L T.
-#a #h #G #L #T #HT elim (cnv_preserve … HT) /2 width=1 by/
+theorem cnv_cpms_conf_lpr (h) (a) (G) (L) (T): IH_cnv_cpms_conf_lpr h a G L T.
+#h #a #G #L #T #HT elim (cnv_preserve … HT) /2 width=1 by/
 qed-.
 
 (* Basic_2A1: uses: snv_cpr_lpr *)
-theorem cnv_cpm_trans_lpr (a) (h) (G) (L) (T): IH_cnv_cpm_trans_lpr a h G L T.
-#a #h #G #L #T #HT elim (cnv_preserve … HT) /2 width=2 by/
+theorem cnv_cpm_trans_lpr (h) (a) (G) (L) (T): IH_cnv_cpm_trans_lpr h a G L T.
+#h #a #G #L #T #HT elim (cnv_preserve … HT) /2 width=2 by/
 qed-.
 
 (* Advanced preservation properties *****************************************)
 
-lemma cnv_cpms_conf (a) (h) (G) (L):
-      â\88\80T0. â¦\83G,Lâ¦\84 â\8a¢ T0 ![a,h] →
-      â\88\80n1,T1. â¦\83G,Lâ¦\84 â\8a¢ T0 â\9e¡*[n1,h] T1 â\86\92 â\88\80n2,T2. â¦\83G,Lâ¦\84 ⊢ T0 ➡*[n2,h] T2 →
-      â\88\83â\88\83T. â¦\83G,Lâ¦\84 â\8a¢ T1 â\9e¡*[n2-n1,h] T & â¦\83G,Lâ¦\84 ⊢ T2 ➡*[n1-n2,h] T.
+lemma cnv_cpms_conf (h) (a) (G) (L):
+      â\88\80T0. â\9dªG,Lâ\9d« â\8a¢ T0 ![h,a] →
+      â\88\80n1,T1. â\9dªG,Lâ\9d« â\8a¢ T0 â\9e¡*[n1,h] T1 â\86\92 â\88\80n2,T2. â\9dªG,Lâ\9d« ⊢ T0 ➡*[n2,h] T2 →
+      â\88\83â\88\83T. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡*[n2-n1,h] T & â\9dªG,Lâ\9d« ⊢ T2 ➡*[n1-n2,h] T.
 /2 width=8 by cnv_cpms_conf_lpr/ qed-.
 
 (* Basic_2A1: uses: snv_cprs_lpr *)
-lemma cnv_cpms_trans_lpr (a) (h) (G) (L) (T): IH_cnv_cpms_trans_lpr a h G L T.
-#a #h #G #L1 #T1 #HT1 #n #T2 #H
+lemma cnv_cpms_trans_lpr (h) (a) (G) (L) (T): IH_cnv_cpms_trans_lpr h a G L T.
+#h #a #G #L1 #T1 #HT1 #n #T2 #H
 @(cpms_ind_dx … H) -n -T2 /3 width=6 by cnv_cpm_trans_lpr/
 qed-.
 
-lemma cnv_cpms_trans (a) (h) (G) (L):
-      ∀T1. ⦃G,L⦄ ⊢ T1 ![a,h] →
-      ∀n,T2. ⦃G,L⦄ ⊢ T1 ➡*[n,h] T2 → ⦃G,L⦄ ⊢ T2 ![a,h].
+lemma cnv_cpm_trans (h) (a) (G) (L):
+      ∀T1. ❪G,L❫ ⊢ T1 ![h,a] →
+      ∀n,T2. ❪G,L❫ ⊢ T1 ➡[n,h] T2 → ❪G,L❫ ⊢ T2 ![h,a].
+/2 width=6 by cnv_cpm_trans_lpr/ qed-.
+
+(* Note: this is the preservation property *)
+lemma cnv_cpms_trans (h) (a) (G) (L):
+      ∀T1. ❪G,L❫ ⊢ T1 ![h,a] →
+      ∀n,T2. ❪G,L❫ ⊢ T1 ➡*[n,h] T2 → ❪G,L❫ ⊢ T2 ![h,a].
 /2 width=6 by cnv_cpms_trans_lpr/ qed-.
+
+lemma cnv_lpr_trans (h) (a) (G):
+      ∀L1,T. ❪G,L1❫ ⊢ T ![h,a] → ∀L2. ❪G,L1❫ ⊢ ➡[h] L2 → ❪G,L2❫ ⊢ T ![h,a].
+/2 width=6 by cnv_cpm_trans_lpr/ qed-.
+
+lemma cnv_lprs_trans (h) (a) (G):
+      ∀L1,T. ❪G,L1❫ ⊢ T ![h,a] → ∀L2. ❪G,L1❫ ⊢ ➡*[h] L2 → ❪G,L2❫ ⊢ T ![h,a].
+#h #a #G #L1 #T #HT #L2 #H
+@(lprs_ind_dx … H) -L2 /2 width=3 by cnv_lpr_trans/
+qed-.