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 l
from proveit.numbers import Add, Exp, LessEq, Mult, Sum, four, frac, one, subtract, 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 = Sum(index_or_indices = sub_expr1, summand = frac(one, Exp(l, two)), domain = _neg_domain)
expr = LessEq(Mult(sub_expr2, Add(sub_expr3, Sum(index_or_indices = sub_expr1, summand = frac(one, Exp(_diff_l_scaled_delta_floor, two)), domain = _pos_domain))), Mult(sub_expr2, Add(sub_expr3, Sum(index_or_indices = sub_expr1, summand = frac(one, Exp(subtract(l, one), two)), 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(\frac{1}{4} \cdot \left(\left(\sum_{l = -2^{t - 1} + 1}^{-\left(e + 1\right)} \frac{1}{l^{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) + \left(\sum_{l = e + 1}^{2^{t - 1}} \frac{1}{\left(l - 1\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: 79 operands: 10
8	Operation	operator: 36 operands: 11
9	Operation	operator: 79 operands: 12
10	ExprTuple	15, 13
11	ExprTuple	87, 14
12	ExprTuple	15, 16
13	Operation	operator: 19 operand: 21
14	Literal
15	Operation	operator: 19 operand: 22
16	Operation	operator: 19 operand: 23
17	ExprTuple	21
18	ExprTuple	22
19	Literal
20	ExprTuple	23
21	Lambda	parameter: 62 body: 24
22	Lambda	parameter: 62 body: 25
23	Lambda	parameter: 62 body: 27
24	Conditional	value: 28 condition: 32
25	Conditional	value: 29 condition: 30
26	ExprTuple	62
27	Conditional	value: 31 condition: 32
28	Operation	operator: 36 operands: 33
29	Operation	operator: 36 operands: 34
30	Operation	operator: 38 operands: 35
31	Operation	operator: 36 operands: 37
32	Operation	operator: 38 operands: 39
33	ExprTuple	87, 40
34	ExprTuple	87, 41
35	ExprTuple	62, 42
36	Literal
37	ExprTuple	87, 43
38	Literal
39	ExprTuple	62, 44
40	Operation	operator: 75 operands: 45
41	Operation	operator: 75 operands: 46
42	Operation	operator: 49 operands: 47
43	Operation	operator: 75 operands: 48
44	Operation	operator: 49 operands: 50
45	ExprTuple	51, 81
46	ExprTuple	62, 81
47	ExprTuple	52, 53
48	ExprTuple	54, 81
49	Literal
50	ExprTuple	61, 67
51	Operation	operator: 79 operands: 55
52	Operation	operator: 79 operands: 56
53	Operation	operator: 85 operand: 61
54	Operation	operator: 79 operands: 58
55	ExprTuple	62, 59
56	ExprTuple	60, 87
57	ExprTuple	61
58	ExprTuple	62, 84
59	Operation	operator: 85 operand: 66
60	Operation	operator: 85 operand: 67
61	Operation	operator: 79 operands: 65
62	Variable
63	ExprTuple	66
64	ExprTuple	67
65	ExprTuple	68, 87
66	Operation	operator: 69 operands: 70
67	Operation	operator: 75 operands: 71
68	Variable
69	Literal
70	ExprTuple	72, 73
71	ExprTuple	81, 74
72	Operation	operator: 75 operands: 76
73	Operation	operator: 77 operand: 82
74	Operation	operator: 79 operands: 80
75	Literal
76	ExprTuple	81, 83
77	Literal
78	ExprTuple	82
79	Literal
80	ExprTuple	83, 84
81	Literal
82	Literal
83	Literal
84	Operation	operator: 85 operand: 87
85	Literal
86	ExprTuple	87
87	Literal