Canonical nat_eqType := Eval hnf in EqType nat nat_eqMixin.
Arguments eqn !m !n.
Arguments eqnP {x y}.

Lemma ltP m n : reflect (m < n)%coq_nat (m < n).
Variant ltn_xor_geq m n : bool -> bool -> Set :=
| LtnNotGeq of m < n  : ltn_xor_geq m n false true
| GeqNotLtn of n <= m : ltn_xor_geq m n true false.