Theorem zfstb1 | index | src |

theorem zfstb1 (n: nat): $ zfst (b1 n) = 0 $;
StepHypRefExpression
1 eqtr
zfst (b1 n) = (\ a2, 0) @ n -> (\ a2, 0) @ n = 0 -> zfst (b1 n) = 0
2 caser
case (\ a1, a1) (\ a2, 0) @ b1 n = (\ a2, 0) @ n
3 2 conv zfst
zfst (b1 n) = (\ a2, 0) @ n
4 1, 3 ax_mp
(\ a2, 0) @ n = 0 -> zfst (b1 n) = 0
5 eqidd
a2 = n -> 0 = 0
6 5 applame
(\ a2, 0) @ n = 0
7 4, 6 ax_mp
zfst (b1 n) = 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)