Theorem ledivmul2 | index | src |

theorem ledivmul2 (a b c: nat): $ c != 0 -> (a <= b // c <-> a * c <= b) $;
StepHypRefExpression
1 leeq1
c * a = a * c -> (c * a <= b <-> a * c <= b)
2 mulcom
c * a = a * c
3 1, 2 ax_mp
c * a <= b <-> a * c <= b
4 ledivmul1
c != 0 -> (a <= b // c <-> c * a <= b)
5 3, 4 syl6bb
c != 0 -> (a <= b // c <-> a * c <= 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)