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

[helm.git] / matita / matita / contribs / lambda_delta / Basic_2 / computation / lsubc.ma

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/computation/lsubc.ma b/matita/matita/contribs/lambda_delta/Basic_2/computation/lsubc.ma
index 60320a22ae35437cfb5c449759b627096735f285..b145a55e100f5adefe0761940b352abddf0508bd 100644 (file)
--- a/matita/matita/contribs/lambda_delta/Basic_2/computation/lsubc.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/computation/lsubc.ma
@@ -27,10 +27,29 @@ interpretation
   "local environment refinement (abstract candidates of reducibility)"
   'CrSubEq L1 RP L2 = (lsubc RP L1 L2).
 
+(* Basic inversion lemmas ***************************************************)
+
+fact lsubc_inv_pair2_aux: ∀RP,L1,L2. L1 [RP] ⊑ L2 → ∀I,K2,W. L2 = K2. 𝕓{I} W →
+                          (∃∃K1. K1 [RP] ⊑ K2 & L1 = K1. 𝕓{I} W) ∨
+                          ∃∃K1,V,A. ⦃K1, V⦄ [RP] ϵ 〚A〛 & ⦃K2, W⦄ [RP] ϵ 〚A〛 & 
+                                    K1 [RP] ⊑ K2 & L1 = K1. 𝕓{Abbr} V &
+                                    I = Abst.
+#RP #L1 #L2 * -L1 -L2
+[ #I #K2 #W #H destruct
+| #J #L1 #L2 #V #HL12 #I #K2 #W #H destruct /3 width=3/
+| #L1 #L2 #V1 #W2 #A #H #HV1 #HW2 #I #K2 #W #H destruct /3 width=7/
+]
+qed.
+
+lemma lsubc_inv_pair2: ∀RP,I,L1,K2,W. L1 [RP] ⊑ K2. 𝕓{I} W →
+                       (∃∃K1. K1 [RP] ⊑ K2 & L1 = K1. 𝕓{I} W) ∨
+                       ∃∃K1,V,A. ⦃K1, V⦄ [RP] ϵ 〚A〛 & ⦃K2, W⦄ [RP] ϵ 〚A〛 & 
+                                 K1 [RP] ⊑ K2 & L1 = K1. 𝕓{Abbr} V &
+                                 I = Abst.
+/2 width=3/ qed-.
+
 (* Basic properties *********************************************************)
 
 lemma lsubc_refl: ∀RP,L. L [RP] ⊑ L.
 #RP #L elim L -L // /2 width=1/
 qed.
-
-(* Basic inversion lemmas ***************************************************)