Theorem dropeqd ≪ | index | src | ≫

theorem dropeqd (_G: wff) (_l1 _l2 _n1 _n2: nat):
  $ _G -> _l1 = _l2 $ >
  $ _G -> _n1 = _n2 $ >
  $ _G -> drop _l1 _n1 = drop _l2 _n2 $;


_G -> i = i
_G -> _n1 = _n2
_G -> i + _n1 = i + _n2
_G -> _l1 = _l2
_G -> nth (i + _n1) _l1 = nth (i + _n2) _l2
_G -> 1 = 1
_G -> nth (i + _n1) _l1 - 1 = nth (i + _n2) _l2 - 1
_G -> \ i, nth (i + _n1) _l1 - 1 == \ i, nth (i + _n2) _l2 - 1
_G -> len _l1 = len _l2
_G -> len _l1 - _n1 = len _l2 - _n2
_G -> lfn (\ i, nth (i + _n1) _l1 - 1) (len _l1 - _n1) = lfn (\ i, nth (i + _n2) _l2 - 1) (len _l2 - _n2)
_G -> drop _l1 _n1 = drop _l2 _n2

Step	Hyp	Ref	Expression
1		eqidd	_G -> i = i
2		hyp _nh	_G -> _n1 = _n2
3	1, 2	addeqd	_G -> i + _n1 = i + _n2
4		hyp _lh	_G -> _l1 = _l2
5	3, 4	ntheqd	_G -> nth (i + _n1) _l1 = nth (i + _n2) _l2
6		eqidd	_G -> 1 = 1
7	5, 6	subeqd	_G -> nth (i + _n1) _l1 - 1 = nth (i + _n2) _l2 - 1
8	7	lameqd	_G -> \ i, nth (i + _n1) _l1 - 1 == \ i, nth (i + _n2) _l2 - 1
9	4	leneqd	_G -> len _l1 = len _l2
10	9, 2	subeqd	_G -> len _l1 - _n1 = len _l2 - _n2
11	8, 10	lfneqd	_G -> lfn (\ i, nth (i + _n1) _l1 - 1) (len _l1 - _n1) = lfn (\ i, nth (i + _n2) _l2 - 1) (len _l2 - _n2)
12	11	conv drop	_G -> drop _l1 _n1 = drop _l2 _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)