Section PROD'.
Variable A : Type.
Variable J_A: Join A.
Variable saA : Perm_alg A.
Variable B: Type.
Variable J_B: Join B.
Variable saB : Perm_alg B.
Variable agB : ageable B.
Variable asb : Age_alg B.

Lemma strong_nat_ind (P : nat -> Prop) (IH : forall n, (forall i, lt i n -> P i) -> P n) n : P n.