theorem appendeq (_l11 _l12 _l21 _l22: nat):
$ _l11 = _l12 -> _l21 = _l22 -> _l11 ++ _l21 = _l12 ++ _l22 $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
anl |
_l11 = _l12 /\ _l21 = _l22 -> _l11 = _l12 |
| 2 |
|
anr |
_l11 = _l12 /\ _l21 = _l22 -> _l21 = _l22 |
| 3 |
1, 2 |
appendeqd |
_l11 = _l12 /\ _l21 = _l22 -> _l11 ++ _l21 = _l12 ++ _l22 |
| 4 |
3 |
exp |
_l11 = _l12 -> _l21 = _l22 -> _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)