closure property S4 added to abstract candidates of reducibility ...

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

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/unfold/ldrops.ma b/matita/matita/contribs/lambda_delta/Basic_2/unfold/ldrops.ma
index 1bf80b5be00702292a3735897fe9203617e8b3ac..254006f1cd541d72dd54a480bbbcb7acc5c03398 100644 (file)
--- a/matita/matita/contribs/lambda_delta/Basic_2/unfold/ldrops.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/unfold/ldrops.ma
@@ -26,6 +26,50 @@ inductive ldrops: list2 nat nat → relation lenv ≝
 interpretation "generic local environment slicing"
    'RDropStar des T1 T2 = (ldrops des T1 T2).
 
+(* Basic inversion lemmas ***************************************************)
+
+fact ldrops_inv_nil_aux: ∀L1,L2,des. ⇩*[des] L1 ≡ L2 → des = ⟠ → L1 = L2.
+#L1 #L2 #des * -L1 -L2 -des //
+#L1 #L #L2 #d #e #des #_ #_ #H destruct
+qed.
+
+lemma ldrops_inv_nil: ∀L1,L2. ⇩*[⟠] L1 ≡ L2 → L1 = L2.
+/2 width=3/ qed-.
+
+fact ldrops_inv_cons_aux: ∀L1,L2,des. ⇩*[des] L1 ≡ L2 →
+                          ∀d,e,tl. des = {d, e} :: tl →
+                          ∃∃L. ⇩*[tl] L1 ≡ L & ⇩[d, e] L ≡ L2.
+#L1 #L2 #des * -L1 -L2 -des
+[ #L #d #e #tl #H destruct
+| #L1 #L #L2 #des #d #e #HT1 #HT2 #hd #he #tl #H destruct
+  /2 width=3/
+qed.
+
+lemma ldrops_inv_cons: ∀L1,L2,d,e,des. ⇩*[{d, e} :: des] L1 ≡ L2 →
+                       ∃∃L. ⇩*[des] L1 ≡ L & ⇩[d, e] L ≡ L2.
+/2 width=3/ qed-.
+
+lemma ldrops_inv_skip2: ∀I,des,i,des2. des ▭ i ≡ des2 →
+                        ∀L1,K2,V2. ⇩*[des2] L1 ≡ K2. 𝕓{I} V2 →
+                        ∃∃K1,V1,des1. des + 1 ▭ i + 1 ≡ des1 + 1 &
+                                      ⇩*[des1] K1 ≡ K2 &
+                                      ⇧*[des1] V2 ≡ V1 &
+                                      L1 = K1. 𝕓{I} V1.
+#I #des #i #des2 #H elim H -des -i -des2
+[ #i #L1 #K2 #V2 #H
+  >(ldrops_inv_nil … H) -L1 /2 width=7/
+| #des #des2 #d #e #i #Hid #_ #IHdes2 #L1 #K2 #V2 #H
+  elim (ldrops_inv_cons … H) -H #L #HL1 #H
+  elim (ldrop_inv_skip2 … H ?) -H /2 width=1/ #K #V >minus_plus #HK2 #HV2 #H destruct
+  elim (IHdes2 … HL1) -IHdes2 -HL1 #K1 #V1 #des1 #Hdes1 #HK1 #HV1 #X destruct
+  @(ex4_3_intro … K1 V1 … ) // [3,4: /2 width=7/ | skip ]
+  normalize >plus_minus // @minuss_lt // /2 width=1/ (**) (* explicit constructors, /3 width=1/ is a bit slow *)
+| #des #des2 #d #e #i #Hid #_ #IHdes2 #L1 #K2 #V2 #H
+  elim (IHdes2 … H) -IHdes2 -H #K1 #V1 #des1 #Hdes1 #HK1 #HV1 #X destruct
+  /4 width=7/
+]
+qed-.
+
 (* Basic properties *********************************************************)
 
 lemma ldrops_skip: ∀L1,L2,des. ⇩*[des] L1 ≡ L2 → ∀V1,V2. ⇧*[des] V2 ≡ V1 →
@@ -40,11 +84,3 @@ qed.
 
 (* Basic_1: removed theorems 1: drop1_getl_trans
 *)
-(*
-lemma ldrops_inv_skip2: ∀des2,L1,I,K2,V2. ⇩*[des2] L1 ≡ K2. 𝕓{I} V2 →
-                        ∀des,i. des ▭ i ≡ des2 →
-                        ∃∃K1,V1,des1. des ▭ (i + 1) ≡ des1 &
-                                      ⇩*[des1] K1 ≡ K2 &
-                                      ⇧*[des1] V2 ≡ V1 &
-                                      L1 = K1. 𝕓{I} V1.
-*)
\ No newline at end of file