Theorem appendsnoc | index | src |

theorem appendsnoc (b l1 l2: nat): $ l1 ++ (l2 |> b) = l1 ++ l2 |> b $;
StepHypRefExpression
1 eqcom
l1 ++ l2 |> b = l1 ++ (l2 |> b) -> l1 ++ (l2 |> b) = l1 ++ l2 |> b
2 appendass
(l1 ++ l2) ++ b : 0 = l1 ++ l2 ++ b : 0
3 2 conv snoc
l1 ++ l2 |> b = l1 ++ (l2 |> b)
4 1, 3 ax_mp
l1 ++ (l2 |> b) = l1 ++ l2 |> 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)