theorem nthext2 (l1 l2 n: nat) {i: nat}:
$ len l1 = n $ >
$ len l2 = n $ >
$ i < n -> nth i l1 = nth i l2 $ >
$ l1 = l2 $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
hyp h1 |
len l1 = n |
| 2 |
1 |
a1i |
T. -> len l1 = n |
| 3 |
|
hyp h2 |
len l2 = n |
| 4 |
3 |
a1i |
T. -> len l2 = n |
| 5 |
|
hyp h3 |
i < n -> nth i l1 = nth i l2 |
| 6 |
5 |
anwr |
T. /\ i < n -> nth i l1 = nth i l2 |
| 7 |
2, 4, 6 |
nthext2d |
T. -> l1 = l2 |
| 8 |
7 |
trud |
l1 = l2 |
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)