support for abstract candidates of reducibility closed! ...

[helm.git] / matita / matita / contribs / lambda_delta / Basic_2 / unfold / lifts_vector.ma

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/unfold/lifts_vector.ma b/matita/matita/contribs/lambda_delta/Basic_2/unfold/lifts_vector.ma
index 3032bc4760d4e4611e1a197123679f062c8eb0eb..2bd579d01dfdeed33cc73df014a01a3be23af21e 100644 (file)
--- a/matita/matita/contribs/lambda_delta/Basic_2/unfold/lifts_vector.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/unfold/lifts_vector.ma
@@ -15,7 +15,7 @@
 include "Basic_2/substitution/lift_vector.ma".
 include "Basic_2/unfold/lifts.ma".
 
-(* GENERIC RELOCATION *******************************************************)
+(* GENERIC TERM VECTOR RELOCATION *******************************************)
 
 inductive liftsv (des:list2 nat nat) : relation (list term) ≝
 | liftsv_nil : liftsv des ◊ ◊
@@ -29,14 +29,23 @@ interpretation "generic relocation (vector)"
 
 (* Basic inversion lemmas ***************************************************)
 
-axiom lifts_inv_applv1: ∀V1s,U1,T2,des. ⇧*[des] Ⓐ V1s. U1 ≡ T2 →
+lemma lifts_inv_applv1: ∀V1s,U1,T2,des. ⇧*[des] Ⓐ V1s. U1 ≡ T2 →
                         ∃∃V2s,U2. ⇧*[des] V1s ≡ V2s & ⇧*[des] U1 ≡ U2 &
                                   T2 = Ⓐ V2s. U2.
+#V1s elim V1s -V1s normalize
+[ #T1 #T2 #des #HT12
+  @(ex3_2_intro) [3,4: // |1,2: skip | // ] (**) (* explicit constructor *)
+| #V1 #V1s #IHV1s #T1 #X #des #H
+  elim (lifts_inv_flat1 … H) -H #V2 #Y #HV12 #HY #H destruct
+  elim (IHV1s … HY) -IHV1s -HY #V2s #T2 #HV12s #HT12 #H destruct
+  @(ex3_2_intro) [4: // |3: /2 width=2/ |1,2: skip | // ] (**) (* explicit constructor *)
+]
+qed-.
 
 (* Basic properties *********************************************************)
 
-lemma liftsv_applv: ∀V1s,V2s,des. ⇧*[des] V1s ≡ V2s →
-                    ∀T1,T2. ⇧*[des] T1 ≡ T2 →
-                    ⇧*[des] Ⓐ V1s. T1 ≡ Ⓐ V2s. T2.
+lemma lifts_applv: ∀V1s,V2s,des. ⇧*[des] V1s ≡ V2s →
+                   ∀T1,T2. ⇧*[des] T1 ≡ T2 →
+                   ⇧*[des] Ⓐ V1s. T1 ≡ Ⓐ V2s. T2.
 #V1s #V2s #des #H elim H -V1s -V2s // /3 width=1/
 qed.