Theorem caseeqd ≪ | index | src | ≫

theorem caseeqd (_G: wff) (_A1 _A2 _B1 _B2: set):
  $ _G -> _A1 == _A2 $ >
  $ _G -> _B1 == _B2 $ >
  $ _G -> case _A1 _B1 == case _A2 _B2 $;

Step	Hyp	Ref	Expression
1		biidd	_G -> (odd n <-> odd n)
2		hyp _Bh	_G -> _B1 == _B2
3		eqidd	_G -> n // 2 = n // 2
4	2, 3	appeqd	_G -> _B1 @ (n // 2) = _B2 @ (n // 2)
5		hyp _Ah	_G -> _A1 == _A2
6	5, 3	appeqd	_G -> _A1 @ (n // 2) = _A2 @ (n // 2)
7	1, 4, 6	ifeqd	_G -> if (odd n) (_B1 @ (n // 2)) (_A1 @ (n // 2)) = if (odd n) (_B2 @ (n // 2)) (_A2 @ (n // 2))
8	7	lameqd	_G -> \ n, if (odd n) (_B1 @ (n // 2)) (_A1 @ (n // 2)) == \ n, if (odd n) (_B2 @ (n // 2)) (_A2 @ (n // 2))
9	8	conv case	_G -> case _A1 _B1 == case _A2 _B2

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)