proposition: Lemma ord_induction_p6 x y: OIax1 -> u <=o x -> ordinalp y -> ordinalp (g (f x y) x).
proof: Proof. move => ax1 ux oy; case: (ozero_dichot oy) => y1. by move: (proj31 ax1 _ ux) => /proj32_1; rewrite y1 fv ord_induction_y0. move: (ord_induction_p41 ax1 ux y1) => h1. exact: (proj32_1(proj33 ax1 _ _ h1 ux)). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)