X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fdynamic%2Fcnv_preserve.ma;h=a7027e195ec234695a8765ea597b271c1946adaf;hb=bd53c4e895203eb049e75434f638f26b5a161a2b;hp=297a86498220e60fbcbf38df9caecd7f8bbe5337;hpb=31be09cc0d040577917783e050e1d38c0daa8f01;p=helm.git

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 297a86498..a7027e195 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve.ma
@@ -19,10 +19,10 @@ 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
+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 ]
@@ -30,67 +30,46 @@ lapply (cnv_fwd_fsb … HT) -HT #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):
-      ∀T0. ⦃G,L⦄ ⊢ T0 ![a,h] →
-      ∀n1,T1. ⦃G,L⦄ ⊢ T0 ➡*[n1,h] T1 → ∀n2,T2. ⦃G,L⦄ ⊢ T0 ➡*[n2,h] T2 →
-      ∃∃T. ⦃G,L⦄ ⊢ T1 ➡*[n2-n1,h] T & ⦃G,L⦄ ⊢ T2 ➡*[n1-n2,h] T.
+lemma cnv_cpms_conf (h) (a) (G) (L):
+      ∀T0. ❪G,L❫ ⊢ T0 ![h,a] →
+      ∀n1,T1. ❪G,L❫ ⊢ T0 ➡*[n1,h] T1 → ∀n2,T2. ❪G,L❫ ⊢ T0 ➡*[n2,h] T2 →
+      ∃∃T. ❪G,L❫ ⊢ T1 ➡*[n2-n1,h] T & ❪G,L❫ ⊢ 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_cpm_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 (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_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 (a) (h) (G):
-      ∀L1,T. ⦃G,L1⦄ ⊢ T ![a,h] → ∀L2. ⦃G,L1⦄ ⊢ ➡[h] L2 → ⦃G,L2⦄ ⊢ T ![a,h].
+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 (a) (h) (G):
-      ∀L1,T. ⦃G,L1⦄ ⊢ T ![a,h] → ∀L2. ⦃G,L1⦄ ⊢ ➡*[h] L2 → ⦃G,L2⦄ ⊢ T ![a,h].
-#a #h #G #L1 #T #HT #L2 #H
+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-.
-
-(* Advanced inversion lemmas ************************************************)
-
-lemma cnv_inv_appl_SO (a) (h) (G) (L):
-      ∀V,T. ⦃G, L⦄ ⊢ ⓐV.T ![a, h] →
-      ∃∃n,p,W0,U0. a = Ⓣ → n = 1 & ⦃G, L⦄ ⊢ V ![a, h] & ⦃G, L⦄ ⊢ T ![a, h] &
-                   ⦃G, L⦄ ⊢ V ➡*[1, h] W0 & ⦃G, L⦄ ⊢ T ➡*[n, h] ⓛ{p}W0.U0.
-* #h #G #L #V #T #H
-elim (cnv_inv_appl … H) -H [ * [| #n ] | #n ] #p #W #U #Ha #HV #HT #HVW #HTU
-[ elim (cnv_fwd_cpm_SO … (ⓛ{p}W.U))
-  [|*: /2 width=8 by cnv_cpms_trans/ ] #X #HU0
-  elim (cpm_inv_abst1 … HU0) #W0 #U0 #HW0 #_ #H0 destruct
-  lapply (cpms_step_dx … HVW … HW0) -HVW -HW0 #HVW0
-  lapply (cpms_step_dx … HTU … HU0) -HTU -HU0 #HTU0
-  /2 width=7 by ex5_4_intro/
-| lapply (Ha ?) -Ha [ // ] #Ha
-  lapply (le_n_O_to_eq n ?) [ /3 width=1 by le_S_S_to_le/ ] -Ha #H destruct
-  /2 width=7 by ex5_4_intro/
-| @(ex5_4_intro … HV HT HVW HTU) #H destruct
-]
-qed-.