- we introduced the pointer_step rc in the perspective of proving

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

diff --git a/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_tstc.ma b/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_tstc.ma
index 59668d4d13aaae036a7abeca498bdb980ab5ccf7..f7afb8df7ca5cd1c46f032a53a64695780d1407d 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_tstc.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_tstc.ma
@@ -14,7 +14,7 @@
 
 include "basic_2/grammar/tstc.ma".
 include "basic_2/computation/cprs_lift.ma".
-include "basic_2/computation/cprs_lcprs.ma".
+include "basic_2/computation/cprs_lfprs.ma".
 
 (* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
 
@@ -26,16 +26,16 @@ lemma cprs_fwd_cnf: ∀L,T. L ⊢ 𝐍⦃T⦄ → ∀U. L ⊢ T ➡* U → T ≃
 qed-.
 
 (* Basic_1: was: pr3_iso_beta *)
-lemma cprs_fwd_beta: ∀L,V,W,T,U. L ⊢ ⓐV. ⓛW. T ➡* U →
-                     ⓐV. ⓛW. T ≃ U ∨ L ⊢ ⓓV. T ➡* U.
-#L #V #W #T #U #H
+lemma cprs_fwd_beta: ∀a,L,V,W,T,U. L ⊢ ⓐV. ⓛ{a}W. T ➡* U →
+                     ⓐV. ⓛ{a}W. T ≃ U ∨ L ⊢ ⓓ{a}V. T ➡* U.
+#a #L #V #W #T #U #H
 elim (cprs_inv_appl1 … H) -H *
 [ #V0 #T0 #_ #_ #H destruct /2 width=1/
-| #V0 #W0 #T0 #HV0 #HT0 #HU
+| #b #V0 #W0 #T0 #HV0 #HT0 #HU
   elim (cprs_inv_abst1 Abbr V … HT0) -HT0 #W1 #T1 #_ #HT1 #H destruct -W1
   @or_intror -W
   @(cprs_trans … HU) -U /2 width=1/ (**) (* explicit constructor *)
-| #V1 #V2 #V0 #T1 #_ #_ #HT1 #_
+| #b #V1 #V2 #V0 #T1 #_ #_ #HT1 #_
   elim (cprs_inv_abst1 Abbr V … HT1) -HT1 #W2 #T2 #_ #_ #H destruct
 ]
 qed-.
@@ -52,40 +52,40 @@ lapply (ldrop_mono … HLK0 … HLK) -HLK0 #H destruct
 lapply (ldrop_fwd_ldrop2 … HLK) -HLK /3 width=9/
 qed-.
 
-lemma cprs_fwd_theta: ∀L,V1,V,T,U. L ⊢ ⓐV1. ⓓV. T ➡* U →
-                      ∀V2. ⇧[0, 1] V1 ≡ V2 → ⓐV1. ⓓV. T ≃ U ∨
-                      L ⊢ ⓓV. ⓐV2. T ➡* U.
-#L #V1 #V #T #U #H #V2 #HV12
+lemma cprs_fwd_theta: ∀a,L,V1,V,T,U. L ⊢ ⓐV1. ⓓ{a}V. T ➡* U →
+                      ∀V2. ⇧[0, 1] V1 ≡ V2 → ⓐV1. ⓓ{a}V. T ≃ U ∨
+                      L ⊢ ⓓ{a}V. ⓐV2. T ➡* U.
+#a #L #V1 #V #T #U #H #V2 #HV12
 elim (cprs_inv_appl1 … H) -H *
 [ -HV12 #V0 #T0 #_ #_ #H destruct /2 width=1/
-| #V0 #W #T0 #HV10 #HT0 #HU
+| #b #V0 #W #T0 #HV10 #HT0 #HU
   elim (cprs_inv_abbr1 … HT0) -HT0 *
   [ #V3 #T3 #_ #_ #H destruct
-  | #X #H #HT2
+  | #X #HT2 #H #H0 destruct
     elim (lift_inv_bind1 … H) -H #W2 #T2 #HW2 #HT02 #H destruct
     @or_intror @(cprs_trans … HU) -U (**) (* explicit constructor *)
-    @(cprs_trans … (ⓓV.ⓐV2.ⓛW2.T2)) [ /3 width=1/ ] -T
-    @(cprs_strap2 … (ⓐV1.ⓛW.T0)) [ /5 width=3/ ] -V -V2 -W2 -T2
-    @(cprs_strap2 … (ⓓV1.T0)) [ /3 width=1/ ] -W /2 width=1/
+    @(cprs_trans … (+ⓓV.ⓐV2.ⓛ{b}W2.T2)) [ /3 width=1/ ] -T
+    @(cprs_strap2 … (ⓐV1.ⓛ{b}W.T0)) [ /5 width=7/ ] -V -V2 -W2 -T2
+    @(cprs_strap2 … (ⓓ{b}V1.T0)) [ /3 width=1/ ] -W /2 width=1/
   ]
-| #V3 #V4 #V0 #T0 #HV13 #HV34 #HT0 #HU
+| #b #V3 #V4 #V0 #T0 #HV13 #HV34 #HT0 #HU
   @or_intror @(cprs_trans … HU) -U (**) (* explicit constructor *)
   elim (cprs_inv_abbr1 … HT0) -HT0 *
   [ #V5 #T5 #HV5 #HT5 #H destruct
     lapply (cprs_lift (L.ⓓV) … HV12 … HV13 … HV34) -V1 -V3 /2 width=1/
     /3 width=1/
-  | #X #H #HT1
+  | #X #HT1 #H #H0 destruct
     elim (lift_inv_bind1 … H) -H #V5 #T5 #HV05 #HT05 #H destruct
     lapply (cprs_lift (L.ⓓV0) … HV12 … HV13 … HV34) -V3 /2 width=1/ #HV24
-    @(cprs_trans … (ⓓV.ⓐV2.ⓓV5.T5)) [ /3 width=1/ ] -T
-    @(cprs_strap2 … (ⓐV1.ⓓV0.T0)) [ /5 width=3/ ] -V -V5 -T5
-    @(cprs_strap2 … (ⓓV0.ⓐV2.T0)) [ /3 width=3/ ] -V1 /3 width=9/
+    @(cprs_trans … (+ⓓV.ⓐV2.ⓓ{b}V5.T5)) [ /3 width=1/ ] -T
+    @(cprs_strap2 … (ⓐV1.ⓓ{b}V0.T0)) [ /5 width=7/ ] -V -V5 -T5
+    @(cprs_strap2 … (ⓓ{b}V0.ⓐV2.T0)) [ /3 width=3/ ] -V1 /3 width=1/
   ]
 ]
 qed-.
 
-lemma cprs_fwd_tau: â\88\80L,W,T,U. L â\8a¢ â\93£W. T ➡* U →
-                    â\93£W. T ≃ U ∨ L ⊢ T ➡* U.
+lemma cprs_fwd_tau: â\88\80L,W,T,U. L â\8a¢ â\93\9dW. T ➡* U →
+                    â\93\9dW. T ≃ U ∨ L ⊢ T ➡* U.
 #L #W #T #U #H
 elim (cprs_inv_cast1 … H) -H /2 width=1/ *
 #W0 #T0 #_ #_ #H destruct /2 width=1/