- we polarized binders to control zeta reduction

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

diff --git a/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_lcprs.ma b/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_lcprs.ma
index 6d4f5ec8cb46f34d3267894288fa163193305bcc..9131ba4c27de4f5f57df3c3475ba1f07ee0c413e 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_lcprs.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_lcprs.ma
@@ -12,8 +12,8 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "Basic_2/computation/cprs_cprs.ma".
-include "Basic_2/computation/lcprs_lcprs.ma".
+include "basic_2/computation/cprs_cprs.ma".
+include "basic_2/computation/lcprs_lcprs.ma".
 
 (* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
 
@@ -25,15 +25,19 @@ lemma lcprs_cprs_trans: ∀L1,L2. L1 ⊢ ➡* L2 →
 #L1 #L2 #HL12 @(lcprs_ind … HL12) -L2 // /3 width=3/
 qed.
 
+lemma lcprs_cpr_trans: ∀L1,L2. L1 ⊢ ➡* L2 →
+                       ∀T1,T2. L2 ⊢ T1 ➡ T2 → L1 ⊢ T1 ➡* T2.
+/3 width=3 by lcprs_cprs_trans, inj/ qed.
+
 (* Advanced inversion lemmas ************************************************)
 
 (* Basic_1: was pr3_gen_abbr *)
-lemma cprs_inv_abbr1: ∀L,V1,T1,U2. L ⊢ ⓓV1. T1 ➡* U2 →
+lemma cprs_inv_abbr1: ∀a,L,V1,T1,U2. L ⊢ ⓓ{a}V1. T1 ➡* U2 →
                       (∃∃V2,T2. L ⊢ V1 ➡* V2 & L. ⓓV1 ⊢ T1 ➡* T2 &
-                                U2 = ⓓV2. T2
+                                U2 = ⓓ{a}V2. T2
                       ) ∨
-                      ∃∃U. ⇧[0, 1] U2 ≡ U & L. ⓓV1 ⊢ T1 ➡* U.
-#L #V1 #T1 #U2 #H @(cprs_ind … H) -U2 /3 width=5/
+                      ∃∃T2. L. ⓓV1 ⊢ T1 ➡* T2 & ⇧[0, 1] U2 ≡ T2 & a = true.
+#a #L #V1 #T1 #U2 #H @(cprs_ind … H) -U2 /3 width=5/
 #U0 #U2 #_ #HU02 * *
 [ #V0 #T0 #HV10 #HT10 #H destruct
   elim (cpr_inv_abbr1 … HU02) -HU02 *
@@ -41,12 +45,12 @@ lemma cprs_inv_abbr1: ∀L,V1,T1,U2. L ⊢ ⓓV1. T1 ➡* U2 →
     lapply (cpr_intro … HV0 … HV2) -HV2 #HV02
     lapply (ltpr_cpr_trans (L.ⓓV0) … HT02) /2 width=1/ -V #HT02
     lapply (lcprs_cprs_trans (L. ⓓV1) … HT02) -HT02 /2 width=1/ /4 width=5/
-  | -V0 #T2 #HT20 #HTU2
-    elim (lift_total U2 0 1) #U0 #HU20
-    lapply (cpr_lift (L.ⓓV1) … HT20 … HU20 HTU2) -T2 /2 width=1/ /4 width=5/
+  | #T2 #HT02 #HUT2
+    lapply (lcprs_cpr_trans (L.ⓓV1) … HT02) -HT02 /2 width=1/ -V0 #HT02
+    lapply (cprs_trans … HT10 … HT02) -T0 /3 width=3/
   ]
-| #U1 #HU01 #HTU1
+| #U1 #HTU1 #HU01
   elim (lift_total U2 0 1) #U #HU2
-  lapply (cpr_lift (L.ⓓV1) … HU01 … HU2 HU02) -U0 /2 width=1/ /4 width=5/
+  lapply (cpr_lift (L.ⓓV1) … HU01 … HU2 HU02) -U0 /2 width=1/ /4 width=3/
 ]
 qed-.