Theorem zfstb0 | index | src |

theorem zfstb0 (n: nat): $ zfst (b0 n) = n $;
StepHypRefExpression
1 eqtr
zfst (b0 n) = (\ a2, a2) @ n -> (\ a2, a2) @ n = n -> zfst (b0 n) = n
2 casel
case (\ a2, a2) (\ a1, 0) @ b0 n = (\ a2, a2) @ n
3 2 conv zfst
zfst (b0 n) = (\ a2, a2) @ n
4 1, 3 ax_mp
(\ a2, a2) @ n = n -> zfst (b0 n) = n
5 id
a2 = n -> a2 = n
6 5 applame
(\ a2, a2) @ n = n
7 4, 6 ax_mp
zfst (b0 n) = 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)