Theorem shreqd ≪ | index | src | ≫

theorem shreqd (_G: wff) (_a1 _a2 _n1 _n2: nat):
  $ _G -> _a1 = _a2 $ >
  $ _G -> _n1 = _n2 $ >
  $ _G -> shr _a1 _n1 = shr _a2 _n2 $;


_G -> _a1 = _a2
_G -> 2 = 2
_G -> _n1 = _n2
_G -> 2 ^ _n1 = 2 ^ _n2
_G -> _a1 // 2 ^ _n1 = _a2 // 2 ^ _n2
_G -> shr _a1 _n1 = shr _a2 _n2

Step	Hyp	Ref	Expression
1		hyp _ah	_G -> _a1 = _a2
2		eqidd	_G -> 2 = 2
3		hyp _nh	_G -> _n1 = _n2
4	2, 3	poweqd	_G -> 2 ^ _n1 = 2 ^ _n2
5	1, 4	diveqd	_G -> _a1 // 2 ^ _n1 = _a2 // 2 ^ _n2
6	5	conv shr	_G -> shr _a1 _n1 = shr _a2 _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)