Theorem rlreceqd ≪ | index | src | ≫

theorem rlreceqd (_G: wff) (_z1 _z2: nat) (_S1 _S2: set) (_n1 _n2: nat):
  $ _G -> _z1 = _z2 $ >
  $ _G -> _S1 == _S2 $ >
  $ _G -> _n1 = _n2 $ >
  $ _G -> rlrec _z1 _S1 _n1 = rlrec _z2 _S2 _n2 $;

Step	Hyp	Ref	Expression
1		hyp _zh	_G -> _z1 = _z2
2		hyp _Sh	_G -> _S1 == _S2
3		eqidd	_G -> rev l, a, ih = rev l, a, ih
4	2, 3	appeqd	_G -> _S1 @ (rev l, a, ih) = _S2 @ (rev l, a, ih)
5	4	lameqd	_G -> \ ih, _S1 @ (rev l, a, ih) == \ ih, _S2 @ (rev l, a, ih)
6	5	slameqd	_G -> (\\ l, \ ih, _S1 @ (rev l, a, ih)) == (\\ l, \ ih, _S2 @ (rev l, a, ih))
7	6	slameqd	_G -> (\\ a, \\ l, \ ih, _S1 @ (rev l, a, ih)) == (\\ a, \\ l, \ ih, _S2 @ (rev l, a, ih))
8		hyp _nh	_G -> _n1 = _n2
9	8	reveqd	_G -> rev _n1 = rev _n2
10	1, 7, 9	lreceqd	_G -> lrec _z1 (\\ a, \\ l, \ ih, _S1 @ (rev l, a, ih)) (rev _n1) = lrec _z2 (\\ a, \\ l, \ ih, _S2 @ (rev l, a, ih)) (rev _n2)
11	10	conv rlrec	_G -> rlrec _z1 _S1 _n1 = rlrec _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)