Theorem mod12 ≪ | index | src | ≫

theorem mod12 (a: nat): $ a % 1 = 0 $;

Step	Hyp	Ref	Expression
1		lt12	a % 1 < 1 <-> a % 1 = 0
2		modlt	1 != 0 -> a % 1 < 1
3		d1ne0	1 != 0
4	2, 3	ax_mp	a % 1 < 1
5	1, 4	mpbi	a % 1 = 0

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), axs_peano (peano1, peano2, peano5, addeq, muleq, add0, addS, mul0, mulS)