proposition: Lemma ord_induction_p12 x b: OIax1 -> u <=o x -> (w0 x) <=o b -> exists y, [/\ y <=o b, (f x y) <=o b & b <o (f x (osucc y))].
proof: Proof. move=> ax1 ux w1b. have ob:= proj32 w1b. case:(normal_ofs_bounded ob (ord_induction_p10 ax1 ux)). by rewrite fv ord_induction_y0 => /(oleNgt w1b). move => [y [py pa pb]]; exists y; split => //. exact (oleT (ord_induction_p9 ax1 ux py) pa). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)