- degree-based equivalene for terms

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc_2A1 / cpr / lift.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cpr/lift.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cpr/lift.etc
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cpr/lift.etc
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+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.
+
+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-.