Theorem zle02 | index | src |

theorem zle02 (a: nat): $ 0 <=Z a <-> ~odd a $;
StepHypRefExpression
1 noteq
(a <Z 0 <-> odd a) -> (~a <Z 0 <-> ~odd a)
2 1 conv zle
(a <Z 0 <-> odd a) -> (0 <=Z a <-> ~odd a)
3 zlt01
a <Z 0 <-> odd a
4 2, 3 ax_mp
0 <=Z a <-> ~odd 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)