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 = Exp(_diff_l_scaled_delta_floor, two)
sub_expr3 = frac(one, sub_expr2)
sub_expr4 = frac(one, Mult(four, sub_expr2))
expr = Equals(Add(Sum(index_or_indices = sub_expr1, summand = sub_expr4, domain = _neg_domain), Sum(index_or_indices = sub_expr1, summand = sub_expr4, domain = _pos_domain)), Mult(frac(one, four), Add(Sum(index_or_indices = sub_expr1, summand = sub_expr3, domain = _neg_domain), Sum(index_or_indices = sub_expr1, summand = sub_expr3, 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(\sum_{l = -2^{t - 1} + 1}^{-\left(e + 1\right)} \frac{1}{4 \cdot \left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}\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(\frac{1}{4} \cdot \left(\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) + \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: 71 operands: 5
4	Operation	operator: 66 operands: 6
5	ExprTuple	7, 8
6	ExprTuple	9, 10
7	Operation	operator: 22 operand: 15
8	Operation	operator: 22 operand: 16
9	Operation	operator: 37 operands: 13
10	Operation	operator: 71 operands: 14
11	ExprTuple	15
12	ExprTuple	16
13	ExprTuple	83, 41
14	ExprTuple	17, 18
15	Lambda	parameter: 57 body: 19
16	Lambda	parameter: 57 body: 20
17	Operation	operator: 22 operand: 25
18	Operation	operator: 22 operand: 26
19	Conditional	value: 24 condition: 32
20	Conditional	value: 24 condition: 34
21	ExprTuple	25
22	Literal
23	ExprTuple	26
24	Operation	operator: 37 operands: 27
25	Lambda	parameter: 57 body: 28
26	Lambda	parameter: 57 body: 30
27	ExprTuple	83, 31
28	Conditional	value: 33 condition: 32
29	ExprTuple	57
30	Conditional	value: 33 condition: 34
31	Operation	operator: 66 operands: 35
32	Operation	operator: 39 operands: 36
33	Operation	operator: 37 operands: 38
34	Operation	operator: 39 operands: 40
35	ExprTuple	41, 43
36	ExprTuple	57, 42
37	Literal
38	ExprTuple	83, 43
39	Literal
40	ExprTuple	57, 44
41	Literal
42	Operation	operator: 47 operands: 45
43	Operation	operator: 73 operands: 46
44	Operation	operator: 47 operands: 48
45	ExprTuple	49, 50
46	ExprTuple	51, 78
47	Literal
48	ExprTuple	56, 62
49	Operation	operator: 71 operands: 52
50	Operation	operator: 81 operand: 56
51	Operation	operator: 71 operands: 54
52	ExprTuple	55, 83
53	ExprTuple	56
54	ExprTuple	57, 58
55	Operation	operator: 81 operand: 62
56	Operation	operator: 71 operands: 60
57	Variable
58	Operation	operator: 81 operand: 64
59	ExprTuple	62
60	ExprTuple	63, 83
61	ExprTuple	64
62	Operation	operator: 73 operands: 65
63	Variable
64	Operation	operator: 66 operands: 67
65	ExprTuple	78, 68
66	Literal
67	ExprTuple	69, 70
68	Operation	operator: 71 operands: 72
69	Operation	operator: 73 operands: 74
70	Operation	operator: 75 operand: 80
71	Literal
72	ExprTuple	79, 77
73	Literal
74	ExprTuple	78, 79
75	Literal
76	ExprTuple	80
77	Operation	operator: 81 operand: 83
78	Literal
79	Literal
80	Literal
81	Literal
82	ExprTuple	83
83	Literal