Section group_morphism.
(* An example with default canonical structures *)
Variable A B : Type.
Variable plusA : A -> A -> A.
Variable plusB : B -> B -> B.
Variable zeroA : A.
Variable zeroB : B.
Variable eqA : A -> A -> Prop.
Variable eqB : B -> B -> Prop.
Variable phi : A -> B.
Record img := {
ia : A;
ib :> B;
prf : phi ia = ib
}.
Parameter eq_img : forall (i1:img) (i2:img),
eqB (ib i1) (ib i2) -> eqA (ia i1) (ia i2).

Lemma phi_img (a:A) : img.