theorem grecaux2eq2d (_G: wff) (z: nat) (_K1 _K2 F: set) (x n k: nat):
$ _G -> _K1 == _K2 $ >
$ _G -> grecaux2 z _K1 F x n k = grecaux2 z _K2 F x n k $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
eqidd |
_G -> z = z |
| 2 |
|
hyp _h |
_G -> _K1 == _K2 |
| 3 |
|
eqsidd |
_G -> F == F |
| 4 |
|
eqidd |
_G -> x = x |
| 5 |
|
eqidd |
_G -> n = n |
| 6 |
|
eqidd |
_G -> k = k |
| 7 |
1, 2, 3, 4, 5, 6 |
grecaux2eqd |
_G -> grecaux2 z _K1 F x n k = grecaux2 z _K2 F x n k |
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)