theorem lfnauxeq (_F1 _F2: set) (_k1 _k2 _n1 _n2: nat):
$ _F1 == _F2 ->
_k1 = _k2 ->
_n1 = _n2 ->
lfnaux _F1 _k1 _n1 = lfnaux _F2 _k2 _n2 $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
anl |
_F1 == _F2 /\ _k1 = _k2 -> _F1 == _F2 |
| 2 |
1 |
anwl |
_F1 == _F2 /\ _k1 = _k2 /\ _n1 = _n2 -> _F1 == _F2 |
| 3 |
|
anr |
_F1 == _F2 /\ _k1 = _k2 -> _k1 = _k2 |
| 4 |
3 |
anwl |
_F1 == _F2 /\ _k1 = _k2 /\ _n1 = _n2 -> _k1 = _k2 |
| 5 |
|
anr |
_F1 == _F2 /\ _k1 = _k2 /\ _n1 = _n2 -> _n1 = _n2 |
| 6 |
2, 4, 5 |
lfnauxeqd |
_F1 == _F2 /\ _k1 = _k2 /\ _n1 = _n2 -> lfnaux _F1 _k1 _n1 = lfnaux _F2 _k2 _n2 |
| 7 |
6 |
exp |
_F1 == _F2 /\ _k1 = _k2 -> _n1 = _n2 -> lfnaux _F1 _k1 _n1 = lfnaux _F2 _k2 _n2 |
| 8 |
7 |
exp |
_F1 == _F2 -> _k1 = _k2 -> _n1 = _n2 -> lfnaux _F1 _k1 _n1 = lfnaux _F2 _k2 _n2 |
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)