proposition: Lemma hole_r_varUD : forall E k p p', p > k -> p = S p' -> E |= p :! -> (initialSeg E k ++ finalSeg E (S k)) |= p' :! .
proof: Proof. intros. apply (proj1 (proj2 (equiv_hole_r E H H0))); trivial. Qed.
imports: CoLoR(RelExtras ListExtras TermsLifting LogicUtil OptUtil) Coq(Arith Setoid Morphisms Lia)