Theorem ocase0 | index | src |

theorem ocase0 (S: set) (z: nat): $ ocase z S @ 0 = z $;
StepHypRefExpression
1 eqtr
ocase z S @ 0 = recn z (\ a1, S @ fst a1) 0 -> recn z (\ a1, S @ fst a1) 0 = z -> ocase z S @ 0 = z
2 ocaseval
ocase z S @ 0 = recn z (\ a1, S @ fst a1) 0
3 1, 2 ax_mp
recn z (\ a1, S @ fst a1) 0 = z -> ocase z S @ 0 = z
4 recn0
recn z (\ a1, S @ fst a1) 0 = z
5 3, 4 ax_mp
ocase z S @ 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)