theorem Arrayeqd (_G: wff) (_A1 _A2: set) (_n1 _n2: nat):
$ _G -> _A1 == _A2 $ >
$ _G -> _n1 = _n2 $ >
$ _G -> Array _A1 _n1 == Array _A2 _n2 $;
Step | Hyp | Ref | Expression |
1 |
|
eqidd |
_G -> l = l |
2 |
|
hyp _Ah |
_G -> _A1 == _A2 |
3 |
2 |
Listeqd |
_G -> List _A1 == List _A2 |
4 |
1, 3 |
eleqd |
_G -> (l e. List _A1 <-> l e. List _A2) |
5 |
|
eqidd |
_G -> len l = len l |
6 |
|
hyp _nh |
_G -> _n1 = _n2 |
7 |
5, 6 |
eqeqd |
_G -> (len l = _n1 <-> len l = _n2) |
8 |
4, 7 |
aneqd |
_G -> (l e. List _A1 /\ len l = _n1 <-> l e. List _A2 /\ len l = _n2) |
9 |
8 |
abeqd |
_G -> {l | l e. List _A1 /\ len l = _n1} == {l | l e. List _A2 /\ len l = _n2} |
10 |
9 |
conv Array |
_G -> Array _A1 _n1 == Array _A2 _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)