theorem recneqd (_G: wff) (_z1 _z2: nat) (_S1 _S2: set) (_n1 _n2: nat):
$ _G -> _z1 = _z2 $ >
$ _G -> _S1 == _S2 $ >
$ _G -> _n1 = _n2 $ >
$ _G -> recn _z1 _S1 _n1 = recn _z2 _S2 _n2 $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
hyp _zh |
_G -> _z1 = _z2 |
| 2 |
|
hyp _Sh |
_G -> _S1 == _S2 |
| 3 |
|
hyp _nh |
_G -> _n1 = _n2 |
| 4 |
1, 2, 3 |
recnauxeqd |
_G -> recnaux _z1 _S1 _n1 = recnaux _z2 _S2 _n2 |
| 5 |
4 |
sndeqd |
_G -> snd (recnaux _z1 _S1 _n1) = snd (recnaux _z2 _S2 _n2) |
| 6 |
5 |
conv recn |
_G -> recn _z1 _S1 _n1 = recn _z2 _S2 _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)