Theorem upto0 | index | src |

theorem upto0: $ upto 0 = 0 $;
StepHypRefExpression
1 eqtr
upto 0 = 1 - 1 -> 1 - 1 = 0 -> upto 0 = 0
2 subeq1
2 ^ 0 = 1 -> 2 ^ 0 - 1 = 1 - 1
3 2 conv upto
2 ^ 0 = 1 -> upto 0 = 1 - 1
4 pow0
2 ^ 0 = 1
5 3, 4 ax_mp
upto 0 = 1 - 1
6 1, 5 ax_mp
1 - 1 = 0 -> upto 0 = 0
7 subid
1 - 1 = 0
8 6, 7 ax_mp
upto 0 = 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)