intuition.
rewrite bool_Comp_seq.
eapply ratAdd_leRat_compat.
eapply leRat_trans.
eapply ratMult_leRat_compat.
eapply leRat_refl.
eapply evalDist_le_1.
eapply eqRat_impl_leRat.
eapply ratMult_1_r.
eapply leRat_trans.
eapply ratMult_leRat_compat.
eapply evalDist_le_1.
eapply leRat_refl.
rewrite ratMult_1_l.
unfold orb.
rewrite evalDist_right_ident.
intuition.
Qed.

Theorem ratS_num':
forall n d,
RatIntro (S n) d == (RatIntro 1 d) + (RatIntro n d).