Theorem b0ltb1 | index | src |

theorem b0ltb1 (a b: nat): $ b0 a < b1 b <-> a <= b $;
StepHypRefExpression
1 bicom
(a <= b <-> b0 a < b1 b) -> (b0 a < b1 b <-> a <= b)
2 b1le
a <= b <-> b1 a <= b1 b
3 2 conv b1, lt
a <= b <-> b0 a < b1 b
4 1, 3 ax_mp
b0 a < b1 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_peano (peano1, peano2, peano5, addeq, muleq, add0, addS, mul0, mulS)