theorem revinj (l l2: nat): $ rev l = rev l2 <-> l = l2 $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
eqeq |
rev (rev l) = l -> rev (rev l2) = l2 -> (rev (rev l) = rev (rev l2) <-> l = l2) |
| 2 |
|
revrev |
rev (rev l) = l |
| 3 |
1, 2 |
ax_mp |
rev (rev l2) = l2 -> (rev (rev l) = rev (rev l2) <-> l = l2) |
| 4 |
|
revrev |
rev (rev l2) = l2 |
| 5 |
3, 4 |
ax_mp |
rev (rev l) = rev (rev l2) <-> l = l2 |
| 6 |
|
reveq |
rev l = rev l2 -> rev (rev l) = rev (rev l2) |
| 7 |
5, 6 |
sylib |
rev l = rev l2 -> l = l2 |
| 8 |
|
reveq |
l = l2 -> rev l = rev l2 |
| 9 |
7, 8 |
ibii |
rev l = rev l2 <-> l = 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)