Theorem zsndb1 | index | src |

theorem zsndb1 (n: nat): $ zsnd (b1 n) = suc n $;
StepHypRefExpression
1 eqtr
zsnd (b1 n) = (\ a2, suc a2) @ n -> (\ a2, suc a2) @ n = suc n -> zsnd (b1 n) = suc n
2 caser
case (\ a1, 0) (\ a2, suc a2) @ b1 n = (\ a2, suc a2) @ n
3 2 conv zsnd
zsnd (b1 n) = (\ a2, suc a2) @ n
4 1, 3 ax_mp
(\ a2, suc a2) @ n = suc n -> zsnd (b1 n) = suc n
5 suceq
a2 = n -> suc a2 = suc n
6 5 applame
(\ a2, suc a2) @ n = suc n
7 4, 6 ax_mp
zsnd (b1 n) = 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)