Theorem zdvdb01 | index | src |

theorem zdvdb01 (a b: nat): $ b0 a |Z b <-> a || zabs b $;
StepHypRefExpression
1 dvdeq1
zabs (b0 a) = a -> (zabs (b0 a) || zabs b <-> a || zabs b)
2 1 conv zdvd
zabs (b0 a) = a -> (b0 a |Z b <-> a || zabs b)
3 zabsb0
zabs (b0 a) = a
4 2, 3 ax_mp
b0 a |Z b <-> a || zabs 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)