X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambda_delta%2Fbasic_2%2Fcomputation%2Fcprs_tstc.ma;h=ab8329cbc0bbadb3ea07f5f8b90423a4fc742868;hb=f79d97a42a84f94d37ad9589fcce46149ee23d12;hp=eb59c5f84a44f4e11dbd6b059edb13e54cd485ae;hpb=cb38da6095e3af84131a3ebf47a9f252f34a804c;p=helm.git

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 eb59c5f84..ab8329cbc 100644
--- a/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_tstc.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_tstc.ma
@@ -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-.
@@ -52,34 +52,34 @@ 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-.