fact: Record semi_morph : Prop := mkRmorph { Smorph0 : [cO] == 0; Smorph1 : [cI] == 1; Smorph_add : forall x y, [x +! y] == [x]+[y]; Smorph_mul : forall x y, [x *! y] == [x]*[y]; Smorph_eq : forall x y, x?=!y = true -> [x] == [y] }.
imports: Setoid Morphisms BinPos BinNat