proposition: Fact vec_fill_tail_ge p : k <= pos2nat p -> vec_pos vec_fill_tail p = e.
proof: Proof. intros H; unfold vec_fill_tail; rew vec. destruct (le_lt_dec k (pos2nat p)); auto; exfalso; lia. Qed.
imports: List Arith Bool Lia Eqdep_dec Undecidability.Shared.Libs.DLW.Utils(utils_tac utils_list utils_nat finite) Undecidability.Shared.Libs.DLW.Vec(pos vec) Undecidability.FOL.TRAKHTENBROT(notations utils fol_ops fo_sig fo_terms fo_logic fo_sat)