Theorem izdvd | index | src |

theorem izdvd (a b c: nat): $ c *Z a = b -> a |Z b $;
StepHypRefExpression
1 zdvdmul1
a |Z c *Z a
2 zdvdeq2
c *Z a = b -> (a |Z c *Z a <-> a |Z b)
3 1, 2 mpbii
c *Z a = b -> a |Z 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)