- support for pointwise extensions of a term relation started ...

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / substitution / lift.ma

diff --git a/matita/matita/contribs/lambda_delta/basic_2/substitution/lift.ma b/matita/matita/contribs/lambda_delta/basic_2/substitution/lift.ma
index 3f3f6b0ff518fd14b628720a4e358ef3f7cb83b3..36c353ba9c75cb1a5d6e694426110fd783927646 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/substitution/lift.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/substitution/lift.ma
@@ -35,6 +35,14 @@ inductive lift: nat → nat → relation term ≝
 
 interpretation "relocation" 'RLift d e T1 T2 = (lift d e T1 T2).
 
+definition t_liftable: relation term → Prop ≝
+                       λR. ∀T1,T2. R T1 T2 → ∀U1,d,e. ⇧[d, e] T1 ≡ U1 →
+                       ∀U2. ⇧[d, e] T2 ≡ U2 → R U1 U2.
+
+definition t_deliftable_sn: relation term → Prop ≝
+                            λR. ∀U1,U2. R U1 U2 → ∀T1,d,e. ⇧[d, e] T1 ≡ U1 →
+                            ∃∃T2. ⇧[d, e] T2 ≡ U2 & R T1 T2.
+
 (* Basic inversion lemmas ***************************************************)
 
 fact lift_inv_refl_O2_aux: ∀d,e,T1,T2. ⇧[d, e] T1 ≡ T2 → e = 0 → T1 = T2.
@@ -369,6 +377,24 @@ lemma is_lift_dec: ∀T2,d,e. Decidable (∃T1. ⇧[d,e] T1 ≡ T2).
 ]
 qed.
 
+lemma t_liftable_TC: ∀R. t_liftable R → t_liftable (TC … R).
+#R #HR #T1 #T2 #H elim H -T2
+[ /3 width=7/
+| #T #T2 #_ #HT2 #IHT1 #U1 #d #e #HTU1 #U2 #HTU2
+  elim (lift_total T d e) /3 width=9/
+]
+qed.
+
+lemma t_deliftable_sn_TC: ∀R. t_deliftable_sn R → t_deliftable_sn (TC … R).
+#R #HR #U1 #U2 #H elim H -U2
+[ #U2 #HU12 #T1 #d #e #HTU1
+  elim (HR … HU12 … HTU1) -U1 /3 width=3/
+| #U #U2 #_ #HU2 #IHU1 #T1 #d #e #HTU1
+  elim (IHU1 … HTU1) -U1 #T #HTU #HT1
+  elim (HR … HU2 … HTU) -U /3 width=5/
+]
+qed-. 
+
 (* Basic_1: removed theorems 7:
             lift_head lift_gen_head
             lift_weight_map lift_weight lift_weight_add lift_weight_add_O