Theorem leappendid1 | index | src |

theorem leappendid1 (a b: nat): $ a <= a ++ b $;
StepHypRefExpression
1 leeq1
a ++ 0 = a -> (a ++ 0 <= a ++ b <-> a <= a ++ b)
2 append02
a ++ 0 = a
3 1, 2 ax_mp
a ++ 0 <= a ++ b <-> a <= a ++ b
4 leappend2
0 <= b <-> a ++ 0 <= a ++ b
5 le01
0 <= b
6 4, 5 mpbi
a ++ 0 <= a ++ b
7 3, 6 mpbi
a <= 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)