theorem repeatArray (A: set) (a n: nat): $ a e. A -> repeat a n e. Array A n $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
elArray |
repeat a n e. Array A n <-> repeat a n e. List A /\ len (repeat a n) = n |
| 2 |
|
repeatT |
a e. A -> repeat a n e. List A |
| 3 |
|
repeatlen |
len (repeat a n) = n |
| 4 |
3 |
a1i |
a e. A -> len (repeat a n) = n |
| 5 |
2, 4 |
iand |
a e. A -> repeat a n e. List A /\ len (repeat a n) = n |
| 6 |
1, 5 |
sylibr |
a e. A -> repeat a n e. Array A 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
(peano1,
peano2,
peano5,
addeq,
muleq,
add0,
addS,
mul0,
mulS)