proposition: Theorem eq_rect_word_mult : forall n n' scale w Heq, eq_rect n (fun n => word (n * scale)) w n' Heq = eq_rect (n * scale) (fun n => word n) w (n' * scale) (eq_rect_word_mult_helper _ _ _ Heq).
proof: Proof. intros. destruct Heq. rewrite (UIP_dec eq_nat_dec (eq_rect_word_mult_helper _ _ scale eq_refl) eq_refl). 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