Theorem zsubneg2 ≪ | index | src | ≫

theorem zsubneg2 (a b: nat): $ a -Z -uZ b = a +Z b $;

Step	Hyp	Ref	Expression
1		zaddeq2	-uZ -uZ b = b -> a +Z -uZ -uZ b = a +Z b
2	1	conv zsub	-uZ -uZ b = b -> a -Z -uZ b = a +Z b
3		znegneg	-uZ -uZ b = b
4	2, 3	ax_mp	a -Z -uZ b = a +Z b

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)