Theorem znegsub2 ≪ | index | src | ≫

theorem znegsub2 (a b: nat): $ -uZ a -Z -uZ b = b -Z a $;

Step	Hyp	Ref	Expression
1		eqtr	-uZ a -Z -uZ b = -uZ a +Z b -> -uZ a +Z b = b -Z a -> -uZ a -Z -uZ b = b -Z a
2		zsubneg2	-uZ a -Z -uZ b = -uZ a +Z b
3	1, 2	ax_mp	-uZ a +Z b = b -Z a -> -uZ a -Z -uZ b = b -Z a
4		zaddcom	-uZ a +Z b = b +Z -uZ a
5	4	conv zsub	-uZ a +Z b = b -Z a
6	3, 5	ax_mp	-uZ a -Z -uZ b = b -Z 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)