Theorem ltsubadd2 | index | src |

theorem ltsubadd2 (a b c: nat): $ b <= a -> (a - b < c <-> a < b + c) $;
StepHypRefExpression
1 lteq2
c + b = b + c -> (a < c + b <-> a < b + c)
2 addcom
c + b = b + c
3 1, 2 ax_mp
a < c + b <-> a < b + c
4 ltsubadd
b <= a -> (a - b < c <-> a < c + b)
5 3, 4 syl6bb
b <= a -> (a - b < c <-> a < b + c)

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 (peano2, peano5, addeq, add0, addS)