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 = frac(one, Exp(_diff_l_scaled_delta_floor, two))
sub_expr4 = Sum(index_or_indices = sub_expr1, summand = sub_expr3, domain = _pos_domain)
sub_expr5 = Sum(index_or_indices = sub_expr1, summand = sub_expr3, domain = _neg_domain)
expr = Equals(Mult(sub_expr2, Add(sub_expr5, sub_expr4)), Add(Mult(sub_expr2, sub_expr5), Mult(sub_expr2, sub_expr4))).with_wrapping_at(2)

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())

\begin{array}{c} \begin{array}{l} \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) =  \\ \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) \end{array} \end{array}

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.	()	(2)	('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: 58 operands: 5
4	Operation	operator: 63 operands: 6
5	ExprTuple	14, 7
6	ExprTuple	8, 9
7	Operation	operator: 63 operands: 10
8	Operation	operator: 58 operands: 11
9	Operation	operator: 58 operands: 12
10	ExprTuple	13, 15
11	ExprTuple	14, 13
12	ExprTuple	14, 15
13	Operation	operator: 18 operand: 20
14	Operation	operator: 30 operands: 17
15	Operation	operator: 18 operand: 22
16	ExprTuple	20
17	ExprTuple	75, 21
18	Literal
19	ExprTuple	22
20	Lambda	parameter: 49 body: 23
21	Literal
22	Lambda	parameter: 49 body: 25
23	Conditional	value: 27 condition: 26
24	ExprTuple	49
25	Conditional	value: 27 condition: 28
26	Operation	operator: 32 operands: 29
27	Operation	operator: 30 operands: 31
28	Operation	operator: 32 operands: 33
29	ExprTuple	49, 34
30	Literal
31	ExprTuple	75, 35
32	Literal
33	ExprTuple	49, 36
34	Operation	operator: 39 operands: 37
35	Operation	operator: 65 operands: 38
36	Operation	operator: 39 operands: 40
37	ExprTuple	41, 42
38	ExprTuple	43, 70
39	Literal
40	ExprTuple	48, 54
41	Operation	operator: 63 operands: 44
42	Operation	operator: 73 operand: 48
43	Operation	operator: 63 operands: 46
44	ExprTuple	47, 75
45	ExprTuple	48
46	ExprTuple	49, 50
47	Operation	operator: 73 operand: 54
48	Operation	operator: 63 operands: 52
49	Variable
50	Operation	operator: 73 operand: 56
51	ExprTuple	54
52	ExprTuple	55, 75
53	ExprTuple	56
54	Operation	operator: 65 operands: 57
55	Variable
56	Operation	operator: 58 operands: 59
57	ExprTuple	70, 60
58	Literal
59	ExprTuple	61, 62
60	Operation	operator: 63 operands: 64
61	Operation	operator: 65 operands: 66
62	Operation	operator: 67 operand: 72
63	Literal
64	ExprTuple	71, 69
65	Literal
66	ExprTuple	70, 71
67	Literal
68	ExprTuple	72
69	Operation	operator: 73 operand: 75
70	Literal
71	Literal
72	Literal
73	Literal
74	ExprTuple	75
75	Literal