Theorem consfst | index | src |

theorem consfst (a b: nat): $ fst (a : b - 1) = a $;
StepHypRefExpression
3
suc (a, b) - 1 = a, b
4
conv cons
a : b - 1 = a, b
5
fst (a : b - 1) = fst (a, b)
7
fst (a, b) = a
8
5, 7
fst (a : b - 1) = a

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)