Theorem conssnoc | index | src |

theorem conssnoc (a b l: nat): $ a : (l |> b) = a : l |> b $;
StepHypRefExpression
1 eqcom
a : l |> b = a : (l |> b) -> a : (l |> b) = a : l |> b
2 appendS
a : l ++ b : 0 = a : (l ++ b : 0)
3 2 conv snoc
a : l |> b = a : (l |> b)
4 1, 3 ax_mp
a : (l |> b) = a : l |> 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)