theorem rlameq1 {x: nat} (a b c: nat x):
$ a = b -> \. x e. a, c = \. x e. b, c $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
nseq |
a = b -> a == b |
| 2 |
1 |
reseq2d |
a = b -> (\ x, c) |` a == (\ x, c) |` b |
| 3 |
2 |
lowereqd |
a = b -> lower ((\ x, c) |` a) = lower ((\ x, c) |` b) |
| 4 |
3 |
conv rlam |
a = b -> \. x e. a, c = \. x e. b, c |
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)