theorem listfneqd (_G: wff) (_l1 _l2: nat):
$ _G -> _l1 = _l2 $ >
$ _G -> listfn _l1 = listfn _l2 $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
eqidd |
_G -> 0 = 0 |
| 2 |
|
eqsidd |
_G ->
(\\ a, \\ z, \ f, \. i e. upto (suc (size (Dom f))), if (i = 0) a (f @ (i - 1))) ==
(\\ a, \\ z, \ f, \. i e. upto (suc (size (Dom f))), if (i = 0) a (f @ (i - 1))) |
| 3 |
|
hyp _lh |
_G -> _l1 = _l2 |
| 4 |
1, 2, 3 |
lreceqd |
_G ->
lrec 0 (\\ a, \\ z, \ f, \. i e. upto (suc (size (Dom f))), if (i = 0) a (f @ (i - 1))) _l1 =
lrec 0 (\\ a, \\ z, \ f, \. i e. upto (suc (size (Dom f))), if (i = 0) a (f @ (i - 1))) _l2 |
| 5 |
4 |
conv listfn |
_G -> listfn _l1 = listfn _l2 |
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)