some restyling ...

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/nta_preserve.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/nta_preserve.ma
index b308c118d6ca11150f56b49cb0261bf5ab6145fe..ebc6fd96db1b50b6f73aba63dcd70f8da0c7f37d 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/nta_preserve.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/nta_preserve.ma
@@ -13,7 +13,7 @@
 (**************************************************************************)
 
 include "basic_2/rt_equivalence/cpcs_cpcs.ma".
-include "basic_2/dynamic/cnv_cpcs.ma".
+include "basic_2/dynamic/cnv_preserve_cpcs.ma".
 include "basic_2/dynamic/nta.ma".
 
 (* NATIVE TYPE ASSIGNMENT FOR TERMS *****************************************)
@@ -51,11 +51,51 @@ elim (cnv_inv_appl … H2) #n #p #X1 #X2 #_ #HV #_ #HVX1 #HUX2
 elim (cnv_cpms_conf … HU … HUX0 … HUX2) -HU -HUX2
 <minus_O_n <minus_n_O #X #HX0 #H
 elim (cpms_inv_abst_sn … H) -H #X3 #X4 #HX13 #HX24 #H destruct
-@(cnv_cast … (ⓐV.X0)) [2:|*: /2 width=1 by cpms_appl_dx/ ]
-@(cnv_appl … X3) [4: |*: /2 width=7 by cpms_trans, cpms_cprs_trans/ ]
-#H destruct
+@(cnv_cast … (ⓐV.X0)) [2:|*: /2 width=1 by cpms_appl_dx/ ] (**) (* full auto a bit slow *)
+/3 width=10 by cnv_appl, cpms_trans, cpms_cprs_trans/
 qed.
 
+(* Basic_1: uses: ty3_sred_wcpr0_pr0 *)
+lemma nta_cpr_conf_lpr (a) (h) (G):
+      ∀L1,T1,U. ⦃G,L1⦄ ⊢ T1 :[a,h] U → ∀T2. ⦃G,L1⦄ ⊢ T1 ➡[h] T2 →
+      ∀L2. ⦃G,L1⦄ ⊢ ➡[h] L2 → ⦃G,L2⦄ ⊢ T2 :[a,h] U.
+#a #h #G #L1 #T1 #U #H #T2 #HT12 #L2 #HL12
+/3 width=6 by cnv_cpm_trans_lpr, cpm_cast/
+qed-.
+
+(* Basic_1: uses: ty3_sred_pr2 ty3_sred_pr0 *)
+lemma nta_cpr_conf (a) (h) (G) (L):
+      ∀T1,U. ⦃G,L⦄ ⊢ T1 :[a,h] U →
+      ∀T2. ⦃G,L⦄ ⊢ T1 ➡[h] T2 → ⦃G,L⦄ ⊢ T2 :[a,h] U.
+#a #h #G #L #T1 #U #H #T2 #HT12
+/3 width=6 by cnv_cpm_trans, cpm_cast/
+qed-.
+
+(* Note: this is the preservation property *)
+(* Basic_1: uses: ty3_sred_pr3 ty3_sred_pr1 *)
+lemma nta_cprs_conf (a) (h) (G) (L):
+      ∀T1,U. ⦃G,L⦄ ⊢ T1 :[a,h] U →
+      ∀T2. ⦃G,L⦄ ⊢ T1 ➡*[h] T2 → ⦃G,L⦄ ⊢ T2 :[a,h] U.
+#a #h #G #L #T1 #U #H #T2 #HT12
+/3 width=6 by cnv_cpms_trans, cpms_cast/
+qed-.
+
+(* Basic_1: uses: ty3_cred_pr2 *)
+lemma nta_lpr_conf (a) (h) (G):
+      ∀L1,T,U. ⦃G,L1⦄ ⊢ T :[a,h] U →
+      ∀L2. ⦃G,L1⦄ ⊢ ➡[h] L2 → ⦃G,L2⦄ ⊢ T :[a,h] U.
+#a #h #G #L1 #T #U #HTU #L2 #HL12
+/2 width=3 by cnv_lpr_trans/
+qed-.
+
+(* Basic_1: uses: ty3_cred_pr3 *)
+lemma nta_lprs_conf (a) (h) (G):
+      ∀L1,T,U. ⦃G,L1⦄ ⊢ T :[a,h] U →
+      ∀L2. ⦃G,L1⦄ ⊢ ➡*[h] L2 → ⦃G,L2⦄ ⊢ T :[a,h] U.
+#a #h #G #L1 #T #U #HTU #L2 #HL12
+/2 width=3 by cnv_lprs_trans/
+qed-.
+
 (* Inversion lemmas based on preservation ***********************************)
 
 lemma nta_inv_ldef_sn (a) (h) (G) (K) (V):
@@ -85,7 +125,7 @@ elim (cpms_inv_lref_sn … H2) -H2 *
 qed-.
 
 lemma nta_inv_lref_sn_drops_cnv (a) (h) (G) (L): 
-      ∀X2, i. ⦃G,L⦄ ⊢ #i :[a,h] X2 →
+      ∀X2,i. ⦃G,L⦄ ⊢ #i :[a,h] X2 →
       ∨∨ ∃∃K,V,W,U. ⬇*[i] L ≘ K.ⓓV & ⦃G,K⦄ ⊢ V :[a,h] W & ⬆*[↑i] W ≘ U & ⦃G,L⦄ ⊢ U ⬌*[h] X2 & ⦃G,L⦄ ⊢ X2 ![a,h]
        | ∃∃K,W,U. ⬇*[i] L ≘ K. ⓛW & ⦃G,K⦄ ⊢ W ![a,h] & ⬆*[↑i] W ≘ U & ⦃G,L⦄ ⊢ U ⬌*[h] X2 & ⦃G,L⦄ ⊢ X2 ![a,h].
 #a #h #G #L #X2 #i #H
@@ -128,13 +168,7 @@ lemma nta_inv_appl_sn (h) (G) (L) (X2):
       ∃∃p,W,U. ⦃G,L⦄ ⊢ V :[h] W & ⦃G,L⦄ ⊢ T :[h] ⓛ{p}W.U & ⦃G,L⦄ ⊢ ⓐV.ⓛ{p}W.U ⬌*[h] X2 & ⦃G,L⦄ ⊢ X2 ![h].
 #h #G #L #X2 #V #T #H
 elim (cnv_inv_cast … H) -H #X #HX2 #H1 #HX2 #H2
-elim (cnv_inv_appl … H1) * [ | #n ] #p #W #U #Hn #HV #HT #HVW #HTU
-[ lapply (cnv_cpms_trans … HT … HTU) #H
-  elim (cnv_inv_bind … H) -H #_ #HU
-  elim (cnv_fwd_cpm_SO … HU) #U0 #HU0 -HU
-  lapply (cpms_step_dx … HTU 1 (ⓛ{p}W.U0) ?) -HTU [ /2 width=1 by cpm_bind/ ] #HTU
-| lapply (le_n_O_to_eq n ?) [ /3 width=1 by le_S_S_to_le/ ] -Hn #H destruct
-]
+elim (cnv_inv_appl_pred … H1) #p #W #U #HV #HT #HVW #HTU
 /5 width=11 by cnv_cpms_nta, cnv_cpms_conf_eq, cpcs_cprs_div, cpms_appl_dx, ex4_3_intro/
 qed-.
 
@@ -206,6 +240,19 @@ elim (cpms_inv_cast1 … H2) -H2 [ * || * ]
 ]
 qed-.
 
+(* Basic_1: uses: ty3_gen_lift *)
+(* Note: "⦃G, L⦄ ⊢ U2 ⬌*[h] X2" can be "⦃G, L⦄ ⊢ X2 ➡*[h] U2" *)
+lemma nta_inv_lifts_sn (a) (h) (G):
+      ∀L,T2,X2. ⦃G,L⦄ ⊢ T2 :[a,h] X2 →
+      ∀b,f,K. ⬇*[b,f] L ≘ K → ∀T1. ⬆*[f] T1 ≘ T2 →
+      ∃∃U1,U2. ⦃G,K⦄ ⊢ T1 :[a,h] U1 & ⬆*[f] U1 ≘ U2 & ⦃G,L⦄ ⊢ U2 ⬌*[h] X2 & ⦃G,L⦄ ⊢ X2 ![a,h].
+#a #h #G #L #T2 #X2 #H #b #f #K #HLK #T1 #HT12
+elim (cnv_inv_cast … H) -H #U2 #HX2 #HT2 #HXU2 #HTU2
+lapply (cnv_inv_lifts … HT2 … HLK … HT12) -HT2 #HT1
+elim (cpms_inv_lifts_sn … HTU2 … HLK … HT12) -T2 -HLK #U1 #HU12 #HTU1
+/3 width=5 by cnv_cpms_nta, cpcs_cprs_sn, ex4_2_intro/
+qed-.
+
 (* Forward lemmas based on preservation *************************************)
 
 (* Basic_1: was: ty3_unique *)
@@ -217,3 +264,14 @@ elim (cnv_inv_cast … H2) -H2 #X2 #_ #HT #HUX2 #HTX2
 lapply (cnv_cpms_conf_eq … HT … HTX1 … HTX2) -T #HX12
 /3 width=3 by cpcs_cprs_div, cpcs_cprs_step_sn/
 qed-.
+
+(* Advanced properties ******************************************************)
+
+(* Basic_1: uses: ty3_sconv_pc3 *)
+lemma nta_cpcs_bi (a) (h) (G) (L):
+      ∀T1,U1. ⦃G,L⦄ ⊢ T1 :[a,h] U1 → ∀T2,U2. ⦃G,L⦄ ⊢ T2 :[a,h] U2 →
+      ⦃G,L⦄ ⊢ T1 ⬌*[h] T2 → ⦃G,L⦄ ⊢ U1 ⬌*[h] U2.
+#a #h #G #L #T1 #U1 #HTU1 #T2 #U2 #HTU2 #HT12
+elim (cpcs_inv_cprs … HT12) -HT12 #T0 #HT10 #HT02
+/3 width=6 by nta_mono, nta_cprs_conf/
+qed-.