Section UnionMapEq.
Variables (K : ordType) (V : eqType) (p : pred K).
Variables (T : Type) (m : @UMC.mixin_of K V p T).
Definition unionmap_eq (f1 f2 : UMC T m) :=
match (UMC.from f1), (UMC.from f2) with
| UM.Undef, UM.Undef => true
| UM.Def f1' pf1, UM.Def f2' pf2 => f1' == f2'
| _, _ => false
end.

Lemma unionmap_eqP : Equality.axiom unionmap_eq.