Expression of type Equals

from the theory of proveit.physics.quantum.QPE

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import ExprRange, Variable, l
from proveit.core_expr_types import Len
from proveit.logic import Equals
from proveit.numbers import Exp, Sum, frac, one, two
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _neg_domain, _pos_domain

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = [l]
sub_expr3 = frac(one, Exp(_diff_l_scaled_delta_floor, two))
expr = Equals(Len(operands = [Sum(index_or_indices = sub_expr2, summand = sub_expr3, domain = _neg_domain), Sum(index_or_indices = sub_expr2, summand = sub_expr3, domain = _pos_domain)]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, two)]))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

|\left(\sum_{l = -2^{t - 1} + 1}^{-\left(e + 1\right)} \frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}, \sum_{l = e + 1}^{2^{t - 1}} \frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}\right)| = |\left(1, \ldots, 2\right)|

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10
8	Operation	operator: 12 operand: 15
9	Operation	operator: 12 operand: 16
10	ExprRange	lambda_map: 14 start_index: 71 end_index: 66
11	ExprTuple	15
12	Literal
13	ExprTuple	16
14	Lambda	parameter: 21 body: 21
15	Lambda	parameter: 45 body: 18
16	Lambda	parameter: 45 body: 20
17	ExprTuple	21
18	Conditional	value: 23 condition: 22
19	ExprTuple	45
20	Conditional	value: 23 condition: 24
21	Variable
22	Operation	operator: 28 operands: 25
23	Operation	operator: 26 operands: 27
24	Operation	operator: 28 operands: 29
25	ExprTuple	45, 30
26	Literal
27	ExprTuple	71, 31
28	Literal
29	ExprTuple	45, 32
30	Operation	operator: 35 operands: 33
31	Operation	operator: 61 operands: 34
32	Operation	operator: 35 operands: 36
33	ExprTuple	37, 38
34	ExprTuple	39, 66
35	Literal
36	ExprTuple	44, 50
37	Operation	operator: 59 operands: 40
38	Operation	operator: 69 operand: 44
39	Operation	operator: 59 operands: 42
40	ExprTuple	43, 71
41	ExprTuple	44
42	ExprTuple	45, 46
43	Operation	operator: 69 operand: 50
44	Operation	operator: 59 operands: 48
45	Variable
46	Operation	operator: 69 operand: 52
47	ExprTuple	50
48	ExprTuple	51, 71
49	ExprTuple	52
50	Operation	operator: 61 operands: 53
51	Variable
52	Operation	operator: 54 operands: 55
53	ExprTuple	66, 56
54	Literal
55	ExprTuple	57, 58
56	Operation	operator: 59 operands: 60
57	Operation	operator: 61 operands: 62
58	Operation	operator: 63 operand: 68
59	Literal
60	ExprTuple	67, 65
61	Literal
62	ExprTuple	66, 67
63	Literal
64	ExprTuple	68
65	Operation	operator: 69 operand: 71
66	Literal
67	Literal
68	Literal
69	Literal
70	ExprTuple	71
71	Literal