Theorem ltconsid2 ≪ | index | src | ≫ 

theorem ltconsid2 (a b: nat): $ b < a : b $;
StepHypRefExpression
1 leltsuc 
b <= a, b <-> b < suc (a, b)
2 1 conv cons 
b <= a, b <-> b < a : b
3 leprid2 
b <= a, b
4 2, 3 mpbi 
b < a : 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)