- Properties S3 and S5 of context-sensitive strongly normalizing terms

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / computation / cprs_tstc_vector.ma

diff --git a/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_tstc_vector.ma b/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_tstc_vector.ma
index 2d63620453ff04b48538ea12707c3332802c1fdd..4b65a08df3048224bb532e8e4ca153dcb462a24a 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_tstc_vector.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_tstc_vector.ma
@@ -19,27 +19,79 @@ include "basic_2/computation/cprs_tstc.ma".
 (* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
 
 (* Vector form of forward lemmas involving same top term constructor ********)
-(*
-lemma cpr_fwd_beta_vector: ∀L,V,W,T,U,Vs. L ⊢ ⒶVs. ⓐV. ⓛW. T ➡ U →
-                           ⒶVs. ⓐV. ⓛW. T ≃ U ∨ L ⊢ ⒶVs. ⓓV. T ➡* U.
-#L #V #W #T #U * /2 width=1 by cpr_fwd_beta/
-#V0 #Vs #H
-elim (cpr_inv_appl1_simple … H ?) -H
-[ #V1 #T1 #_ #_ #H destruct /2 width=1/
-| elim Vs -Vs //
+
+(* Basic_1: was: pr3_iso_appls_beta *)
+lemma cprs_fwd_beta_vector: ∀L,Vs,V,W,T,U. L ⊢ ⒶVs. ⓐV. ⓛW. T ➡* U →
+                            ⒶVs. ⓐV. ⓛW. T ≃ U ∨ L ⊢ ⒶVs. ⓓV. T ➡* U.
+#L #Vs elim Vs -Vs /2 width=1 by cprs_fwd_beta/
+#V0 #Vs #IHVs #V #W #T #U #H
+elim (cprs_inv_appl1 … H) -H *
+[ -IHVs #V1 #T1 #_ #_ #H destruct /2 width=1/
+| #V1 #W1 #T1 #HV01 #HT1 #HU
+  elim (IHVs … HT1) -IHVs -HT1 #HT1
+  [ elim (tstc_inv_bind_appls_simple … HT1 ?) //
+  | @or_intror -W (**) (* explicit constructor *)
+    @(cprs_trans … HU) -U
+    @(cprs_strap1 … (ⓐV1.ⓛW1.T1)) [ /2 width=1/ ] -V -V0 -Vs -T /3 width=1/
+  ]
+| #V1 #V2 #V3 #T1 #HV01 #HV12 #HT1 #HU
+  elim (IHVs … HT1) -IHVs -HT1 #HT1
+  [ elim (tstc_inv_bind_appls_simple … HT1 ?) //
+  | @or_intror -W (**) (* explicit constructor *)
+    @(cprs_trans … HU) -U
+    @(cprs_strap1 … (ⓐV1.ⓓV3.T1)) [ /2 width=1/ ] -V -V0 -Vs -T /3 width=3/
+  ]
 ]
 qed-.
 
-lemma cpr_fwd_theta_vector: ∀L,V1s,V2s. ⇧[0, 1] V1s ≡ V2s →
-                            ∀V,T,U. L ⊢ ⒶV1s. ⓓV. T ➡ U →
-                            ⒶV1s. ⓓV. T ≃ U ∨ L ⊢ ⓓV. ⒶV2s. T ➡* U.
+(* Basic_1: was: pr3_iso_appls_abbr *)
+lemma cprs_fwd_theta_vector: ∀L,V1s,V2s. ⇧[0, 1] V1s ≡ V2s →
+                             ∀V,T,U. L ⊢ ⒶV1s. ⓓV. T ➡* U →
+                             ⒶV1s. ⓓV. T ≃ U ∨ L ⊢ ⓓV. ⒶV2s. T ➡* U.
 #L #V1s #V2s * -V1s -V2s /3 width=1/
-#V1s #V2s #V1a #V2a #HV12a * -V1s -V2s /2 width=1 by cpr_fwd_theta/ -HV12a
-#V1s #V2s #V1b #V2b #_ #_ #V #U #T #H
-elim (cpr_inv_appl1_simple … H ?) -H //
-#V0 #T0 #_ #_ #H destruct /2 width=1/
+#V1s #V2s #V1a #V2a #HV12a #HV12s
+generalize in match HV12a; -HV12a
+generalize in match V2a; -V2a
+generalize in match V1a; -V1a
+elim HV12s -V1s -V2s /2 width=1 by cprs_fwd_theta/
+#V1s #V2s #V1b #V2b #HV12b #_ #IHV12s #V1a #V2a #HV12a #V #T #U #H
+elim (cprs_inv_appl1 … H) -H *
+[ -IHV12s -HV12a -HV12b #V0 #T0 #_ #_ #H destruct /2 width=1/
+| #V0a #W0 #T0 #HV10a #HT0 #HU
+  elim (IHV12s … HV12b … HT0) -IHV12s -HT0 #HT0
+  [ -HV12a -HV12b -HV10a -HU
+    elim (tstc_inv_pair1 … HT0) #V1 #T1 #H destruct
+  | @or_intror -V1s (**) (* explicit constructor *)
+    @(cprs_trans … HU) -U
+    elim (cprs_inv_abbr1 … HT0) -HT0 *
+    [ -HV12a -HV12b -HV10a #V1 #T1 #_ #_ #H destruct
+    | -V1b #X #H #HT1
+      elim (lift_inv_bind1 … H) -H #W1 #T1 #HW01 #HT01 #H destruct
+      @(cprs_trans … (ⓓV.ⓐV2a.ⓛW1.T1)) [ /3 width=1/ ] -T -V2b -V2s
+      @(cprs_strap2 … (ⓐV1a.ⓛW0.T0)) [ /5 width=3/ ] -V -V2a -W1 -T1
+      @(cprs_strap2 … (ⓓV1a.T0)) [ /3 width=1/ ] -W0 /2 width=1/
+    ]
+  ]
+| #V0a #Va #V0 #T0 #HV10a #HV0a #HT0 #HU
+  elim (IHV12s … HV12b … HT0) -HV12b -IHV12s -HT0 #HT0
+  [ -HV12a -HV10a -HV0a -HU
+    elim (tstc_inv_pair1 … HT0) #V1 #T1 #H destruct
+  | @or_intror -V1s -V1b (**) (* explicit constructor *)
+    @(cprs_trans … HU) -U
+    elim (cprs_inv_abbr1 … HT0) -HT0 *
+    [ #V1 #T1 #HV1 #HT1 #H destruct
+      lapply (cprs_lift (L.ⓓV) … HV12a … HV10a … HV0a) -V1a -V0a [ /2 width=1/ ] #HV2a
+      @(cprs_trans … (ⓓV.ⓐV2a.T1)) [ /3 width=1/ ] -T -V2b -V2s /3 width=1/
+    | #X #H #HT1
+      elim (lift_inv_bind1 … H) -H #V1 #T1 #HW01 #HT01 #H destruct
+      lapply (cprs_lift (L.ⓓV0) … HV12a … HV10a … HV0a) -V0a [ /2 width=1/ ] #HV2a
+      @(cprs_trans … (ⓓV.ⓐV2a.ⓓV1.T1)) [ /3 width=1/ ] -T -V2b -V2s
+      @(cprs_strap2 … (ⓐV1a.ⓓV0.T0)) [ /5 width=3/ ] -V -V1 -T1
+      @(cprs_strap2 … (ⓓV0.ⓐV2a.T0)) [ /3 width=3/ ] -V1a /3 width=1/
+    ]
+  ]
+]  
 qed-.
-*)
 
 (* Basic_1: was: pr3_iso_appls_cast *)
 lemma cprs_fwd_tau_vector: ∀L,Vs,W,T,U. L ⊢ ⒶVs. ⓣW. T ➡* U →
@@ -51,19 +103,15 @@ elim (cprs_inv_appl1 … H) -H *
 | #V0 #W0 #T0 #HV0 #HT0 #HU
   elim (IHVs … HT0) -IHVs -HT0 #HT0
   [ elim (tstc_inv_bind_appls_simple … HT0 ?) //
-  | @or_intror
-    @(cprs_trans … HU) -HU
-    @(cprs_strap1 … (ⓐV0.ⓛW0.T0)) /2 width=1/ -HV0 -HT0 /3 width=1/
+  | @or_intror -W (**) (* explicit constructor *)
+    @(cprs_trans … HU) -U
+    @(cprs_strap1 … (ⓐV0.ⓛW0.T0)) [ /2 width=1/ ] -V -Vs -T /3 width=1/
   ]
 | #V0 #V1 #V2 #T0 #HV0 #HV01 #HT0 #HU
   elim (IHVs … HT0) -IHVs -HT0 #HT0
   [ elim (tstc_inv_bind_appls_simple … HT0 ?) //
-  | @or_intror
-    @(cprs_trans … HU) -HU
-    @(cprs_strap1 … (ⓐV0.ⓓV2.T0)) /2 width=1/ -HV0 -HT0 /3 width=3/
+  | @or_intror -W (**) (* explicit constructor *)
+    @(cprs_trans … HU) -U
+    @(cprs_strap1 … (ⓐV0.ⓓV2.T0)) [ /2 width=1/ ] -V -Vs -T /3 width=3/
 ]
 qed-.
-
-axiom cprs_fwd_theta_vector: ∀L,V1s,V2s. ⇧[0, 1] V1s ≡ V2s →
-                            ∀V,T,U. L ⊢ ⒶV1s. ⓓV. T ➡* U →
-                            ⒶV1s. ⓓV. T ≃ U ∨ L ⊢ ⓓV. ⒶV2s. T ➡* U.