theorem elArray (A: set) (l n: nat):
$ l e. Array A n <-> l e. List A /\ len l = n $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
eleq1 |
x = l -> (x e. List A <-> l e. List A) |
| 2 |
|
leneq |
x = l -> len x = len l |
| 3 |
2 |
eqeq1d |
x = l -> (len x = n <-> len l = n) |
| 4 |
1, 3 |
aneqd |
x = l -> (x e. List A /\ len x = n <-> l e. List A /\ len l = n) |
| 5 |
4 |
elabe |
l e. {x | x e. List A /\ len x = n} <-> l e. List A /\ len l = n |
| 6 |
5 |
conv Array |
l e. Array A n <-> l e. List A /\ len l = n |
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)