Theorem b1lt | index | src |

theorem b1lt (a b: nat): $ a < b <-> b1 a < b1 b $;
StepHypRefExpression
1 bitr
(a < b <-> b0 a < b0 b) -> (b0 a < b0 b <-> b1 a < b1 b) -> (a < b <-> b1 a < b1 b)
2 b0lt
a < b <-> b0 a < b0 b
3 1, 2 ax_mp
(b0 a < b0 b <-> b1 a < b1 b) -> (a < b <-> b1 a < b1 b)
4 ltsuc
b0 a < b0 b <-> suc (b0 a) < suc (b0 b)
5 4 conv b1
b0 a < b0 b <-> b1 a < b1 b
6 3, 5 ax_mp
a < b <-> b1 a < b1 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)