theorem caseeq (_A1 _A2 _B1 _B2: set):
$ _A1 == _A2 -> _B1 == _B2 -> case _A1 _B1 == case _A2 _B2 $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
anl |
_A1 == _A2 /\ _B1 == _B2 -> _A1 == _A2 |
| 2 |
|
anr |
_A1 == _A2 /\ _B1 == _B2 -> _B1 == _B2 |
| 3 |
1, 2 |
caseeqd |
_A1 == _A2 /\ _B1 == _B2 -> case _A1 _B1 == case _A2 _B2 |
| 4 |
3 |
exp |
_A1 == _A2 -> _B1 == _B2 -> case _A1 _B1 == case _A2 _B2 |
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)