proposition: Lemma existT_wplus: forall sz (w1 w2: word sz) sz' (w3 w4: word sz'), existT word _ w1 = existT word _ w3 -> existT word _ w2 = existT word _ w4 -> existT word _ (w1 ^+ w2) = existT word _ (w3 ^+ w4).
proof: Proof. intros. rewrite eq_sigT_sig_eq in H; destruct H as [Hsz1 ?]. rewrite eq_sigT_sig_eq in H0; destruct H0 as [Hsz2 ?]. subst; do 2 rewrite <-(eq_rect_eq_dec eq_nat_dec). 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