theorem ljoineqd (_G: wff) (_L1 _L2: nat):
$ _G -> _L1 = _L2 $ >
$ _G -> ljoin _L1 = ljoin _L2 $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
eqidd |
_G -> 0 = 0 |
| 2 |
|
eqsidd |
_G -> (\\ a, \\ z, \ ih, a ++ ih) == (\\ a, \\ z, \ ih, a ++ ih) |
| 3 |
|
hyp _Lh |
_G -> _L1 = _L2 |
| 4 |
1, 2, 3 |
lreceqd |
_G -> lrec 0 (\\ a, \\ z, \ ih, a ++ ih) _L1 = lrec 0 (\\ a, \\ z, \ ih, a ++ ih) _L2 |
| 5 |
4 |
conv ljoin |
_G -> ljoin _L1 = ljoin _L2 |
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
(peano2,
addeq,
muleq)