Theorem zlt01 ≪ | index | src | ≫

theorem zlt01 (a: nat): $ a  odd a $;

Step	Hyp	Ref	Expression
1		oddeq	a -Z 0 = a -> (odd (a -Z 0) <-> odd a)
2	1	conv zlt	a -Z 0 = a -> (a <Z 0 <-> odd a)
3		zsub02	a -Z 0 = a
4	2, 3	ax_mp	a <Z 0 <-> odd a

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp, itru), axs_pred_calc (ax_gen, ax_4, ax_5, ax_6, ax_7, ax_10, ax_11, ax_12), axs_set (elab, ax_8), axs_the (theid, the0), axs_peano (peano1, peano2, peano5, addeq, muleq, add0, addS, mul0, mulS)