Section ContraLeq.
Implicit Types (b : bool) (m n : nat) (P : Prop).
Definition trecE := (addE, (doubleE, oddE), (mulE, add_mulE, (expE, mul_expE))).
End NatTrec.
Notation natTrecE := NatTrec.trecE.

Lemma eq_binP : Equality.axiom N.eqb.