Theorem conssnd | index | src |

theorem conssnd (a b: nat): $ snd (a : b - 1) = b $;
StepHypRefExpression
1 eqtr
snd (a : b - 1) = snd (a, b) -> snd (a, b) = b -> snd (a : b - 1) = b
2 sndeq
a : b - 1 = a, b -> snd (a : b - 1) = snd (a, b)
3 sucsub1
suc (a, b) - 1 = a, b
4 3 conv cons
a : b - 1 = a, b
5 2, 4 ax_mp
snd (a : b - 1) = snd (a, b)
6 1, 5 ax_mp
snd (a, b) = b -> snd (a : b - 1) = b
7 sndpr
snd (a, b) = b
8 6, 7 ax_mp
snd (a : b - 1) = b

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)