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, Sum, 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 = Sum(index_or_indices = sub_expr1, summand = frac(one, Exp(l, two)), domain = _neg_domain)
expr = LessEq(Add(sub_expr2, Sum(index_or_indices = sub_expr1, summand = frac(one, Exp(_diff_l_scaled_delta_floor, two)), domain = _pos_domain)), Add(sub_expr2, 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(\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) \leq \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)

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: 72 operands: 5
4	Operation	operator: 72 operands: 6
5	ExprTuple	8, 7
6	ExprTuple	8, 9
7	Operation	operator: 12 operand: 14
8	Operation	operator: 12 operand: 15
9	Operation	operator: 12 operand: 16
10	ExprTuple	14
11	ExprTuple	15
12	Literal
13	ExprTuple	16
14	Lambda	parameter: 55 body: 17
15	Lambda	parameter: 55 body: 18
16	Lambda	parameter: 55 body: 20
17	Conditional	value: 21 condition: 25
18	Conditional	value: 22 condition: 23
19	ExprTuple	55
20	Conditional	value: 24 condition: 25
21	Operation	operator: 29 operands: 26
22	Operation	operator: 29 operands: 27
23	Operation	operator: 31 operands: 28
24	Operation	operator: 29 operands: 30
25	Operation	operator: 31 operands: 32
26	ExprTuple	80, 33
27	ExprTuple	80, 34
28	ExprTuple	55, 35
29	Literal
30	ExprTuple	80, 36
31	Literal
32	ExprTuple	55, 37
33	Operation	operator: 68 operands: 38
34	Operation	operator: 68 operands: 39
35	Operation	operator: 42 operands: 40
36	Operation	operator: 68 operands: 41
37	Operation	operator: 42 operands: 43
38	ExprTuple	44, 74
39	ExprTuple	55, 74
40	ExprTuple	45, 46
41	ExprTuple	47, 74
42	Literal
43	ExprTuple	54, 60
44	Operation	operator: 72 operands: 48
45	Operation	operator: 72 operands: 49
46	Operation	operator: 78 operand: 54
47	Operation	operator: 72 operands: 51
48	ExprTuple	55, 52
49	ExprTuple	53, 80
50	ExprTuple	54
51	ExprTuple	55, 77
52	Operation	operator: 78 operand: 59
53	Operation	operator: 78 operand: 60
54	Operation	operator: 72 operands: 58
55	Variable
56	ExprTuple	59
57	ExprTuple	60
58	ExprTuple	61, 80
59	Operation	operator: 62 operands: 63
60	Operation	operator: 68 operands: 64
61	Variable
62	Literal
63	ExprTuple	65, 66
64	ExprTuple	74, 67
65	Operation	operator: 68 operands: 69
66	Operation	operator: 70 operand: 75
67	Operation	operator: 72 operands: 73
68	Literal
69	ExprTuple	74, 76
70	Literal
71	ExprTuple	75
72	Literal
73	ExprTuple	76, 77
74	Literal
75	Literal
76	Literal
77	Operation	operator: 78 operand: 80
78	Literal
79	ExprTuple	80
80	Literal