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 l
from proveit.logic import Equals
from proveit.numbers import Add, Exp, Mult, Sum, four, 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 = [l]
sub_expr2 = frac(one, four)
sub_expr3 = Exp(_diff_l_scaled_delta_floor, two)
sub_expr4 = frac(one, sub_expr3)
sub_expr5 = Mult(sub_expr2, Sum(index_or_indices = sub_expr1, summand = sub_expr4, domain = _neg_domain))
expr = Equals(Add(sub_expr5, Sum(index_or_indices = sub_expr1, summand = frac(one, Mult(four, sub_expr3)), domain = _pos_domain)), Add(sub_expr5, Mult(sub_expr2, Sum(index_or_indices = sub_expr1, summand = sub_expr4, domain = _pos_domain))))

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(\left(\frac{1}{4} \cdot \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}}\right)\right) + \left(\sum_{l = e + 1}^{2^{t - 1}} \frac{1}{4 \cdot \left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}\right)\right) = \left(\left(\frac{1}{4} \cdot \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}}\right)\right) + \left(\frac{1}{4} \cdot \left(\sum_{l = e + 1}^{2^{t - 1}} \frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}\right)\right)\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: 69 operands: 5
4	Operation	operator: 69 operands: 6
5	ExprTuple	8, 7
6	ExprTuple	8, 9
7	Operation	operator: 20 operand: 13
8	Operation	operator: 64 operands: 11
9	Operation	operator: 64 operands: 12
10	ExprTuple	13
11	ExprTuple	15, 14
12	ExprTuple	15, 16
13	Lambda	parameter: 55 body: 17
14	Operation	operator: 20 operand: 23
15	Operation	operator: 35 operands: 19
16	Operation	operator: 20 operand: 24
17	Conditional	value: 22 condition: 32
18	ExprTuple	23
19	ExprTuple	81, 39
20	Literal
21	ExprTuple	24
22	Operation	operator: 35 operands: 25
23	Lambda	parameter: 55 body: 26
24	Lambda	parameter: 55 body: 28
25	ExprTuple	81, 29
26	Conditional	value: 31 condition: 30
27	ExprTuple	55
28	Conditional	value: 31 condition: 32
29	Operation	operator: 64 operands: 33
30	Operation	operator: 37 operands: 34
31	Operation	operator: 35 operands: 36
32	Operation	operator: 37 operands: 38
33	ExprTuple	39, 41
34	ExprTuple	55, 40
35	Literal
36	ExprTuple	81, 41
37	Literal
38	ExprTuple	55, 42
39	Literal
40	Operation	operator: 45 operands: 43
41	Operation	operator: 71 operands: 44
42	Operation	operator: 45 operands: 46
43	ExprTuple	47, 48
44	ExprTuple	49, 76
45	Literal
46	ExprTuple	54, 60
47	Operation	operator: 69 operands: 50
48	Operation	operator: 79 operand: 54
49	Operation	operator: 69 operands: 52
50	ExprTuple	53, 81
51	ExprTuple	54
52	ExprTuple	55, 56
53	Operation	operator: 79 operand: 60
54	Operation	operator: 69 operands: 58
55	Variable
56	Operation	operator: 79 operand: 62
57	ExprTuple	60
58	ExprTuple	61, 81
59	ExprTuple	62
60	Operation	operator: 71 operands: 63
61	Variable
62	Operation	operator: 64 operands: 65
63	ExprTuple	76, 66
64	Literal
65	ExprTuple	67, 68
66	Operation	operator: 69 operands: 70
67	Operation	operator: 71 operands: 72
68	Operation	operator: 73 operand: 78
69	Literal
70	ExprTuple	77, 75
71	Literal
72	ExprTuple	76, 77
73	Literal
74	ExprTuple	78
75	Operation	operator: 79 operand: 81
76	Literal
77	Literal
78	Literal
79	Literal
80	ExprTuple	81
81	Literal