theorem ljoinsnoc (L l: nat): $ ljoin (L |> l) = ljoin L ++ l $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
eqtr |
ljoin (L |> l) = ljoin L ++ ljoin (l : 0) -> ljoin L ++ ljoin (l : 0) = ljoin L ++ l -> ljoin (L |> l) = ljoin L ++ l |
| 2 |
|
ljoinappend |
ljoin (L ++ l : 0) = ljoin L ++ ljoin (l : 0) |
| 3 |
2 |
conv snoc |
ljoin (L |> l) = ljoin L ++ ljoin (l : 0) |
| 4 |
1, 3 |
ax_mp |
ljoin L ++ ljoin (l : 0) = ljoin L ++ l -> ljoin (L |> l) = ljoin L ++ l |
| 5 |
|
appendeq2 |
ljoin (l : 0) = l -> ljoin L ++ ljoin (l : 0) = ljoin L ++ l |
| 6 |
|
ljoin1 |
ljoin (l : 0) = l |
| 7 |
5, 6 |
ax_mp |
ljoin L ++ ljoin (l : 0) = ljoin L ++ l |
| 8 |
4, 7 |
ax_mp |
ljoin (L |> l) = ljoin L ++ l |
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)