Theorem zpncan3 | index | src |

theorem zpncan3 (a b: nat): $ a +Z (b -Z a) = b $;
StepHypRefExpression
1 eqtr
a +Z (b -Z a) = b -Z a +Z a -> b -Z a +Z a = b -> a +Z (b -Z a) = b
2 zaddcom
a +Z (b -Z a) = b -Z a +Z a
3 1, 2 ax_mp
b -Z a +Z a = b -> a +Z (b -Z a) = b
4 znpcan
b -Z a +Z a = b
5 3, 4 ax_mp
a +Z (b -Z a) = 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)