theorem appendeqd (_G: wff) (_l11 _l12 _l21 _l22: nat):
$ _G -> _l11 = _l12 $ >
$ _G -> _l21 = _l22 $ >
$ _G -> _l11 ++ _l21 = _l12 ++ _l22 $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
hyp _l2h |
_G -> _l21 = _l22 |
| 2 |
|
eqsidd |
_G -> (\\ x, \\ z, \ y, x : y) == (\\ x, \\ z, \ y, x : y) |
| 3 |
|
hyp _l1h |
_G -> _l11 = _l12 |
| 4 |
1, 2, 3 |
lreceqd |
_G -> lrec _l21 (\\ x, \\ z, \ y, x : y) _l11 = lrec _l22 (\\ x, \\ z, \ y, x : y) _l12 |
| 5 |
4 |
conv append |
_G -> _l11 ++ _l21 = _l12 ++ _l22 |
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)