- basics: some support for abstract triangular confluence (which

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

diff --git a/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_cprs.ma b/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_cprs.ma
index 16c1a6256164a873d0b3c143a4d6b32163d2459e..518c2bd07295a88765cbe26ed0a2785cfaf8971e 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_cprs.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_cprs.ma
@@ -12,10 +12,10 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "Basic_2/reducibility/cpr_lift.ma".
-include "Basic_2/reducibility/cpr_cpr.ma".
-include "Basic_2/reducibility/lcpr_cpr.ma".
-include "Basic_2/computation/cprs_lcpr.ma".
+include "basic_2/reducibility/cpr_lift.ma".
+include "basic_2/reducibility/cpr_cpr.ma".
+include "basic_2/reducibility/lcpr_cpr.ma".
+include "basic_2/computation/cprs_lcpr.ma".
 
 (* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
 
@@ -40,6 +40,11 @@ lemma cpr_abbr2: ∀L,V1,V2. L ⊢ V1 ➡ V2 → ∀T1,T2. L. ⓓV2 ⊢ T1 ➡ T
 lapply (lcpr_cpr_trans (L. ⓓV1) … HT12) /2 width=1/
 qed.
 
+(* Basic_1: was: pr3_strip *)
+lemma cprs_strip: ∀L,T1,T. L ⊢ T ➡* T1 → ∀T2. L ⊢ T ➡ T2 →
+                  ∃∃T0. L ⊢ T1 ➡ T0 & L ⊢ T2 ➡* T0.
+/3 width=3/ qed.
+
 (* Advanced inversion lemmas ************************************************)
 
 (* Basic_1: was pr3_gen_appl *)
@@ -75,6 +80,7 @@ theorem cprs_conf: ∀L,T1,T. L ⊢ T ➡* T1 → ∀T2. L ⊢ T ➡* T2 →
 theorem cprs_trans: ∀L,T1,T. L ⊢ T1 ➡* T → ∀T2. L ⊢ T ➡* T2 → L ⊢ T1 ➡* T2.
 /2 width=3/ qed.
 
+(* Basic_1: was: pr3_flat *)
 lemma cprs_flat: ∀I,L,T1,T2. L ⊢ T1 ➡* T2 → ∀V1,V2. L ⊢ V1 ➡* V2 →
                  L ⊢ ⓕ{I} V1. T1 ➡* ⓕ{I} V2. T2.
 #I #L #T1 #T2 #HT12 #V1 #V2 #HV12 @(cprs_ind … HV12) -V2 /2 width=1/
@@ -82,6 +88,13 @@ lemma cprs_flat: ∀I,L,T1,T2. L ⊢ T1 ➡* T2 → ∀V1,V2. L ⊢ V1 ➡* V2 
 @(cprs_trans … IHV1) -IHV1 /2 width=1/ 
 qed.
 
+lemma cprs_abbr: ∀L,V1,T1,T2. L. ⓓV1 ⊢ T1 ➡* T2 → ∀V2. L ⊢ V1 ➡* V2 →
+                 L ⊢ ⓓV1. T1 ➡* ⓓV2. T2.
+#L #V1 #T1 #T2 #HT12 #V2 #HV12 @(cprs_ind … HV12) -V2 /2 width=1/
+#V #V2 #_ #HV2 #IHV1
+@(cprs_trans … IHV1) -IHV1 /2 width=1/
+qed.
+
 (* Basic_1: was only: pr3_pr2_pr3_t pr3_wcpr0_t *)
 lemma lcpr_cprs_trans: ∀L1,L2. L1 ⊢ ➡ L2 →
                        ∀T1,T2. L2 ⊢ T1 ➡* T2 → L1 ⊢ T1 ➡* T2.