Theorem zle0sub | index | src |

theorem zle0sub (a b: nat): $ 0 <=Z a -Z b <-> b <=Z a $;
StepHypRefExpression
1 noteq
(a -Z b <Z 0 <-> a <Z b) -> (~a -Z b <Z 0 <-> ~a <Z b)
2 1 conv zle
(a -Z b <Z 0 <-> a <Z b) -> (0 <=Z a -Z b <-> b <=Z a)
3 zltsub0
a -Z b <Z 0 <-> a <Z b
4 2, 3 ax_mp
0 <=Z a -Z 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)