Theorem zleadd2 | index | src |

theorem zleadd2 (a b c: nat): $ b <=Z c <-> a +Z b <=Z a +Z c $;
StepHypRefExpression
1 noteq
(c <Z b <-> a +Z c <Z a +Z b) -> (~c <Z b <-> ~a +Z c <Z a +Z b)
2 1 conv zle
(c <Z b <-> a +Z c <Z a +Z b) -> (b <=Z c <-> a +Z b <=Z a +Z c)
3 zltadd2
c <Z b <-> a +Z c <Z a +Z b
4 2, 3 ax_mp
b <=Z c <-> a +Z b <=Z a +Z c

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)