theorem writeeq (_F1 _F2: set) (_a1 _a2 _b1 _b2: nat):
$ _F1 == _F2 ->
_a1 = _a2 ->
_b1 = _b2 ->
write _F1 _a1 _b1 == write _F2 _a2 _b2 $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
anl |
_F1 == _F2 /\ _a1 = _a2 -> _F1 == _F2 |
| 2 |
1 |
anwl |
_F1 == _F2 /\ _a1 = _a2 /\ _b1 = _b2 -> _F1 == _F2 |
| 3 |
|
anr |
_F1 == _F2 /\ _a1 = _a2 -> _a1 = _a2 |
| 4 |
3 |
anwl |
_F1 == _F2 /\ _a1 = _a2 /\ _b1 = _b2 -> _a1 = _a2 |
| 5 |
|
anr |
_F1 == _F2 /\ _a1 = _a2 /\ _b1 = _b2 -> _b1 = _b2 |
| 6 |
2, 4, 5 |
writeeqd |
_F1 == _F2 /\ _a1 = _a2 /\ _b1 = _b2 -> write _F1 _a1 _b1 == write _F2 _a2 _b2 |
| 7 |
6 |
exp |
_F1 == _F2 /\ _a1 = _a2 -> _b1 = _b2 -> write _F1 _a1 _b1 == write _F2 _a2 _b2 |
| 8 |
7 |
exp |
_F1 == _F2 -> _a1 = _a2 -> _b1 = _b2 -> write _F1 _a1 _b1 == write _F2 _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)