Expression of type LessEq

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 Variable, l
from proveit.numbers import Add, Exp, LessEq, 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))
expr = LessEq(Mult(sub_expr2, 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))), Mult(sub_expr2, Add(Sum(index_or_indices = sub_expr1, summand = frac(one, Exp(l, two)), domain = _neg_domain), Variable("_a", latex_format = r"{_{-}a}"))))

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