proposition: Lemma sext_wplus_wordToZ_distr_existT: forall sz (w1 w2: word sz) ssz (sw1 sw2: word ssz) n, existT word _ w1 = existT word _ (sext sw1 n) -> existT word _ w2 = existT word _ (sext sw2 n) -> n <> 0 -> wordToZ (w1 ^+ w2) = (wordToZ w1 + wordToZ w2)%Z.
proof: Proof. intros. assert (sz = ssz + n) by (apply eq_sigT_fst in H; auto); subst. destruct_existT. apply sext_wplus_wordToZ_distr; auto. 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