Theorem repeat1 | index | src |

theorem repeat1 (a: nat): $ repeat a 1 = a : 0 $;
StepHypRefExpression
1 eqtr
repeat a 1 = a : repeat a 0 -> a : repeat a 0 = a : 0 -> repeat a 1 = a : 0
2 repeatS
repeat a (suc 0) = a : repeat a 0
3 2 conv d1
repeat a 1 = a : repeat a 0
4 1, 3 ax_mp
a : repeat a 0 = a : 0 -> repeat a 1 = a : 0
5 conseq2
repeat a 0 = 0 -> a : repeat a 0 = a : 0
6 repeat0
repeat a 0 = 0
7 5, 6 ax_mp
a : repeat a 0 = a : 0
8 4, 7 ax_mp
repeat a 1 = a : 0

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)