Theorem revsn | index | src |

theorem revsn (a: nat): $ rev (a : 0) = a : 0 $;
StepHypRefExpression
1 eqtr
rev (a : 0) = rev 0 |> a -> rev 0 |> a = a : 0 -> rev (a : 0) = a : 0
2 revS
rev (a : 0) = rev 0 |> a
3 1, 2 ax_mp
rev 0 |> a = a : 0 -> rev (a : 0) = a : 0
4 eqtr
rev 0 |> a = 0 |> a -> 0 |> a = a : 0 -> rev 0 |> a = a : 0
5 snoceq1
rev 0 = 0 -> rev 0 |> a = 0 |> a
6 rev0
rev 0 = 0
7 5, 6 ax_mp
rev 0 |> a = 0 |> a
8 4, 7 ax_mp
0 |> a = a : 0 -> rev 0 |> a = a : 0
9 snoc0
0 |> a = a : 0
10 8, 9 ax_mp
rev 0 |> a = a : 0
11 3, 10 ax_mp
rev (a : 0) = a : 0

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)