- predefined_virtuals: some additions

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

diff --git a/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_lift.ma b/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_lift.ma
index ccff2f1feafeea00e1ad0534bd42a2927f2ad2e1..11ce81ff8e1706e18f9a8cedd97c0ad78041e641 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_lift.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/computation/cprs_lift.ma
@@ -12,11 +12,41 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "Basic_2/reducibility/cpr_lift.ma".
-include "Basic_2/computation/cprs.ma".
+include "basic_2/reducibility/cpr_lift.ma".
+include "basic_2/computation/cprs.ma".
 
 (* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
 
+(* Advanced inversion lemmas ************************************************)
+
+(* Basic_1: was: pr3_gen_lref *)
+lemma cprs_inv_lref1: ∀L,T2,i. L ⊢ #i ➡* T2 →
+                      T2 = #i ∨
+                      ∃∃K,V1,T1. ⇩[0, i] L ≡ K. ⓓV1 &
+                                 K ⊢ V1 ➡* T1 &
+                                 ⇧[0, i + 1] T1 ≡ T2 &
+                                 i < |L|.
+#L #T2 #i #H @(cprs_ind … H) -T2 /2 width=1/
+#T #T2 #_ #HT2 *
+[ #H destruct
+  elim (cpr_inv_lref1 … HT2) -HT2 /2 width=1/
+  * #K #V1 #T1 #HLK #HVT1 #HT12 #Hi
+  @or_intror @(ex4_3_intro … HLK … HT12) // /3 width=3/ (**) (* explicit constructors *)
+| * #K #V1 #T1 #HLK #HVT1 #HT1 #Hi
+  lapply (ldrop_fwd_ldrop2 … HLK) #H0LK
+  elim (cpr_inv_lift … H0LK … HT1 … HT2) -H0LK -T /4 width=6/
+]
+qed-.
+
+(* Basic_1: was: pr3_gen_abst *)
+lemma cprs_inv_abst1: ∀I,W,L,V1,T1,U2. L ⊢ ⓛV1. T1 ➡* U2 →
+                      ∃∃V2,T2. L ⊢ V1 ➡* V2 & L. ⓑ{I} W ⊢ T1 ➡* T2 &
+                               U2 = ⓛV2. T2.
+#I #W #L #V1 #T1 #U2 #H @(cprs_ind … H) -U2 /2 width=5/
+#U #U2 #_ #HU2 * #V #T #HV1 #HT1 #H destruct
+elim (cpr_inv_abst1 … HU2 I W) -HU2 #V2 #T2 #HV2 #HT2 #H destruct  /3 width=5/
+qed-.
+
 (* Relocation properties ****************************************************)
 
 (* Basic_1: was: pr3_lift *)