Theorem muldivle | index | src |

theorem muldivle (a b: nat): $ b * (a // b) <= a $;
StepHypRefExpression
1 leeq2
b * (a // b) + a % b = a -> (b * (a // b) <= b * (a // b) + a % b <-> b * (a // b) <= a)
2 divmod
b * (a // b) + a % b = a
3 1, 2 ax_mp
b * (a // b) <= b * (a // b) + a % b <-> b * (a // b) <= a
4 leaddid1
b * (a // b) <= b * (a // b) + a % b
5 3, 4 mpbi
b * (a // b) <= 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)