Theorem ltsubeq0 | index | src |

theorem ltsubeq0 (a b: nat): $ a < b -> a - b = 0 $;
StepHypRefExpression
1 ltnle
a < b <-> ~b <= a
2 nlesubeq0
~b <= a -> a - b = 0
3 1, 2 sylbi
a < b -> a - b = 0

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, add0, addS)