proposition: Theorem wtl_match : forall n n' (w : word (S n)) (Heq : S n = S n') (Heq' : n = n'), (match Heq' in (_ = N) return (word N) with | eq_refl => wtl w end) = wtl (match Heq in (_ = N) return (word N) with | eq_refl => w end).
proof: Proof. intros. repeat match goal with | [ |- context[match ?pf with refl_equal => _ end] ] => generalize pf end. generalize dependent w; clear. intros. generalize Heq Heq'. subst. intros. rewrite (UIP_dec eq_nat_dec Heq' (refl_equal _)). rewrite (UIP_dec eq_nat_dec Heq0 (refl_equal _)). reflexivity. Qed.
imports: Coq.Classes.Morphisms Coq.Classes.Morphisms_Prop Coq.Classes.Equivalence Coq.Arith.PeanoNat Coq.ZArith.BinInt  Coq.Arith.Arith Coq.NArith.NArith Coq.Bool.Bool Coq.ZArith.ZArith Coq.Logic.Eqdep_dec Coq.Logic.EqdepFacts Coq.Program.Tactics Coq.Program.Equality Coq.setoid_ring.Ring Coq.setoid_ring.Ring_polynom bbv.Nomega bbv.ZLib bbv.NatLib bbv.NLib bbv.N_Z_nat_conversions bbv.DepEq bbv.DepEqNat bbv.ReservedNotations Coq.micromega.Lia