auxiliary update in basic_2

[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 ab3b33ad5675415276e73e442d97020695a87799..464e8603a20da1e494b64f9025511679a79fbbc4 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/nta_preserve.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/nta_preserve.ma
@@ -31,6 +31,17 @@ elim (cnv_fwd_cpm_SO … HT) #U #HTU
 /4 width=2 by cnv_cpms_nta, cpm_cpms, ex_intro/
 qed-.
 
+(* Basic_1: was: ty3_typecheck *)
+lemma nta_typecheck (a) (h) (G) (L):
+      ∀T,U. ⦃G,L⦄ ⊢ T :[a,h] U → ∃T0. ⦃G,L⦄ ⊢ ⓝU.T :[a,h] T0.
+/3 width=1 by cnv_cast, cnv_nta_sn/ qed-.
+
+(* Basic_1: was: ty3_correct *)
+(* Basic_2A1: was: ntaa_fwd_correct *)
+lemma nta_fwd_correct (a) (h) (G) (L):
+      ∀T,U. ⦃G,L⦄ ⊢ T :[a,h] U → ∃T0. ⦃G,L⦄ ⊢ U :[a,h] T0.
+/3 width=2 by nta_fwd_cnv_dx, cnv_nta_sn/ qed-.
+
 lemma nta_pure_cnv (h) (G) (L):
       ∀T,U. ⦃G,L⦄ ⊢ T :*[h] U →
       ∀V. ⦃G,L⦄ ⊢ ⓐV.U !*[h] → ⦃G,L⦄ ⊢ ⓐV.T :*[h] ⓐV.U.
@@ -83,6 +94,31 @@ elim (cnv_cpms_conf … H1 … H2 … HVTU) -H1 -H2 -HVTU <minus_n_n #X0 #HX0 #H
 /3 width=5 by cprs_div, cprs_trans/
 qed-.
 
+lemma nta_inv_pure_sn_cnv (h) (G) (L) (X2):
+                          ∀V,T. ⦃G,L⦄ ⊢ ⓐV.T :*[h] X2 →
+                          ∨∨ ∃∃p,W,T0,U0. ⦃G,L⦄ ⊢ V :*[h] W & ⦃G,L⦄ ⊢ ⓛ{p}W.T0 :*[h] ⓛ{p}W.U0 & ⦃G,L⦄ ⊢ T ➡*[h] ⓛ{p}W.T0 & ⦃G,L⦄ ⊢ ⓐV.ⓛ{p}W.U0 ⬌*[h] X2 & ⦃G,L⦄ ⊢ X2 !*[h]
+                           | ∃∃U. ⦃G,L⦄ ⊢ T :*[h] U & ⦃G,L⦄ ⊢ ⓐV.U !*[h] & ⦃G,L⦄ ⊢ ⓐV.U ⬌*[h] X2 & ⦃G,L⦄ ⊢ X2 !*[h].
+#h #G #L #X2 #V #T #H
+elim (cnv_inv_cast … H) -H #X1 #HX2 #H1 #HX21 #H
+elim (cnv_inv_appl … H1) -H1 * [| #n ] #p #W0 #T0 #_ #HV #HT #HW0 #HT0
+lapply (cnv_cpms_trans … HT … HT0) #H
+elim (cnv_inv_bind … H) -H #_ #H1T0
+[ elim (cpms_inv_appl_sn_decompose … H) -H #U #HTU #HUX1 
+  
+
+  [ #V0 #U0 #HV0 #HU0 #H destruct
+    elim (cnv_cpms_conf … HT … HT0 … HU0)
+    <minus_O_n <minus_n_O #X #H #HU0X
+    elim (cpms_inv_abst_sn … H) -H #W1 #U1 #HW01 #HU01 #H destruct
+    @or_introl
+    @(ex5_4_intro … U1 … HT0 … HX2) -HX2
+    [ /2 width=1 by cnv_cpms_nta/
+    | @nta_bind_cnv /2 width=4 by cnv_cpms_trans/ /2 width=3 by cnv_cpms_nta/
+    | @(cpcs_cprs_div … HX21) -HX21
+      @(cprs_div … (ⓐV0.ⓛ{p}W1.U1))
+      /3 width=1 by cpms_appl, cpms_appl_dx, cpms_bind/ 
+    ]
+  
 (* Basic_2A1: uses: nta_inv_cast1 *)
 lemma nta_inv_cast_sn (a) (h) (G) (L) (X2):
       ∀U,T. ⦃G,L⦄ ⊢ ⓝU.T :[a,h] X2 →
@@ -106,6 +142,32 @@ elim (cpms_inv_cast1 … H2) -H2 [ * || * ]
 ]
 qed-.
 
+(* Basic_1: uses: ty3_gen_cast *)
+lemma nta_inv_cast_sn_old (a) (h) (G) (L) (X2):
+      ∀T0,T1. ⦃G,L⦄ ⊢ ⓝT1.T0 :[a,h] X2 →
+      ∃∃T2. ⦃G,L⦄ ⊢ T0 :[a,h] T1 & ⦃G,L⦄ ⊢ T1 :[a,h] T2 & ⦃G,L⦄ ⊢ ⓝT2.T1 ⬌*[h] X2 & ⦃G,L⦄ ⊢ X2 ![a,h].
+#a #h #G #L #X2 #T0 #T1 #H
+elim (cnv_inv_cast … H) -H #X0 #HX2 #H1 #HX20 #H2
+elim (cnv_inv_cast … H1) #X #HT1 #HT0 #HT1X #HT0X
+elim (cpms_inv_cast1 … H2) -H2 [ * || * ]
+[ #U1 #U0 #HTU1 #HTU0 #H destruct
+  elim (cnv_cpms_conf … HT0 … HT0X … HTU0) -HT0 -HT0X -HTU0
+  <minus_n_n #X0 #HX0 #HUX0
+  lapply (cprs_trans … HT1X … HX0) -X #HT1X0
+  /5 width=7 by cnv_cpms_nta, cpcs_cprs_div, cprs_div, cpms_cast, ex4_intro/
+| #HTX0
+  elim (cnv_cpms_conf … HT0 … HT0X … HTX0) -HT0 -HT0X -HTX0
+  <minus_n_n #X1 #HX1 #HX01
+  elim (cnv_nta_sn … HT1) -HT1 #U1 #HTU1
+  lapply (cprs_trans … HT1X … HX1) -X #HTX1
+  lapply (cprs_trans … HX20 … HX01) -X0 #HX21
+  /4 width=5 by cprs_div, cpms_eps, ex4_intro/
+| #n #HT1X0 #H destruct -X -HT0
+  elim (cnv_nta_sn … HT1) -HT1 #U1 #HTU1
+  /4 width=5 by cprs_div, cpms_eps, ex4_intro/
+]
+qed-.
+
 (* Forward lemmas based on preservation *************************************)
 
 (* Basic_1: was: ty3_unique *)