theorem takeeqd (_G: wff) (_l1 _l2 _n1 _n2: nat):
$ _G -> _l1 = _l2 $ >
$ _G -> _n1 = _n2 $ >
$ _G -> take _l1 _n1 = take _l2 _n2 $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
hyp _lh |
_G -> _l1 = _l2 |
| 2 |
1 |
ntheq2d |
_G -> nth i _l1 = nth i _l2 |
| 3 |
2 |
subeq1d |
_G -> nth i _l1 - 1 = nth i _l2 - 1 |
| 4 |
3 |
lameqd |
_G -> \ i, nth i _l1 - 1 == \ i, nth i _l2 - 1 |
| 5 |
1 |
leneqd |
_G -> len _l1 = len _l2 |
| 6 |
|
hyp _nh |
_G -> _n1 = _n2 |
| 7 |
5, 6 |
mineqd |
_G -> min (len _l1) _n1 = min (len _l2) _n2 |
| 8 |
4, 7 |
lfneqd |
_G -> lfn (\ i, nth i _l1 - 1) (min (len _l1) _n1) = lfn (\ i, nth i _l2 - 1) (min (len _l2) _n2) |
| 9 |
8 |
conv take |
_G -> take _l1 _n1 = take _l2 _n2 |
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)