theorem greceqd (_G: wff) (_z1 _z2: nat) (_K1 _K2 _F1 _F2: set)
(_n1 _n2 _k1 _k2: nat):
$ _G -> _z1 = _z2 $ >
$ _G -> _K1 == _K2 $ >
$ _G -> _F1 == _F2 $ >
$ _G -> _n1 = _n2 $ >
$ _G -> _k1 = _k2 $ >
$ _G -> grec _z1 _K1 _F1 _n1 _k1 = grec _z2 _K2 _F2 _n2 _k2 $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
hyp _zh |
_G -> _z1 = _z2 |
| 2 |
|
hyp _Kh |
_G -> _K1 == _K2 |
| 3 |
|
hyp _Fh |
_G -> _F1 == _F2 |
| 4 |
|
hyp _nh |
_G -> _n1 = _n2 |
| 5 |
|
hyp _kh |
_G -> _k1 = _k2 |
| 6 |
1, 2, 3, 4, 4, 5 |
grecaux2eqd |
_G -> grecaux2 _z1 _K1 _F1 _n1 _n1 _k1 = grecaux2 _z2 _K2 _F2 _n2 _n2 _k2 |
| 7 |
6 |
conv grec |
_G -> grec _z1 _K1 _F1 _n1 _k1 = grec _z2 _K2 _F2 _n2 _k2 |
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)