Theorem recnaux0 | index | src |

theorem recnaux0 (S: set) (z: nat): $ recnaux z S 0 = 0, z $;
StepHypRefExpression
1 rec0
rec (0, z) (\ a1, suc (fst a1), S @ a1) 0 = 0, z
2 1 conv recnaux
recnaux z S 0 = 0, z

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)