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, 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, Exp(_diff_l_scaled_delta_floor, two))
sub_expr3 = Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = _pos_domain)
expr = LessEq(Add(Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = _neg_domain), sub_expr3), Add(Sum(index_or_indices = sub_expr1, summand = frac(one, Exp(l, two)), domain = _neg_domain), sub_expr3))

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}{\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) \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 - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\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: 62 operands: 5
4	Operation	operator: 62 operands: 6
5	ExprTuple	7, 9
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: 48 body: 17
15	Lambda	parameter: 48 body: 18
16	Lambda	parameter: 48 body: 20
17	Conditional	value: 23 condition: 22
18	Conditional	value: 21 condition: 22
19	ExprTuple	48
20	Conditional	value: 23 condition: 24
21	Operation	operator: 27 operands: 25
22	Operation	operator: 29 operands: 26
23	Operation	operator: 27 operands: 28
24	Operation	operator: 29 operands: 30
25	ExprTuple	74, 31
26	ExprTuple	48, 32
27	Literal
28	ExprTuple	74, 33
29	Literal
30	ExprTuple	48, 34
31	Operation	operator: 64 operands: 35
32	Operation	operator: 38 operands: 36
33	Operation	operator: 64 operands: 37
34	Operation	operator: 38 operands: 39
35	ExprTuple	48, 69
36	ExprTuple	40, 41
37	ExprTuple	42, 69
38	Literal
39	ExprTuple	47, 53
40	Operation	operator: 62 operands: 43
41	Operation	operator: 72 operand: 47
42	Operation	operator: 62 operands: 45
43	ExprTuple	46, 74
44	ExprTuple	47
45	ExprTuple	48, 49
46	Operation	operator: 72 operand: 53
47	Operation	operator: 62 operands: 51
48	Variable
49	Operation	operator: 72 operand: 55
50	ExprTuple	53
51	ExprTuple	54, 74
52	ExprTuple	55
53	Operation	operator: 64 operands: 56
54	Variable
55	Operation	operator: 57 operands: 58
56	ExprTuple	69, 59
57	Literal
58	ExprTuple	60, 61
59	Operation	operator: 62 operands: 63
60	Operation	operator: 64 operands: 65
61	Operation	operator: 66 operand: 71
62	Literal
63	ExprTuple	70, 68
64	Literal
65	ExprTuple	69, 70
66	Literal
67	ExprTuple	71
68	Operation	operator: 72 operand: 74
69	Literal
70	Literal
71	Literal
72	Literal
73	ExprTuple	74
74	Literal