Theorem optupto | index | src |

theorem optupto (n: nat): $ Option (upto n) == upto (suc n) $;
StepHypRefExpression
1 eqstr4
Option (upto n) == b1 (upto n) -> upto (suc n) == b1 (upto n) -> Option (upto n) == upto (suc n)
2 optns
Option (upto n) == b1 (upto n)
3 1, 2 ax_mp
upto (suc n) == b1 (upto n) -> Option (upto n) == upto (suc n)
4 nseq
upto (suc n) = b1 (upto n) -> upto (suc n) == b1 (upto n)
5 uptoS
upto (suc n) = b1 (upto n)
6 4, 5 ax_mp
upto (suc n) == b1 (upto n)
7 3, 6 ax_mp
Option (upto n) == upto (suc n)

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)