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 e, l
from proveit.numbers import Add, Exp, LessEq, Mult, Sum, four, frac, one, two
from proveit.physics.quantum.QPE import Pfail, _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))
expr = LessEq(Pfail(e), Mult(frac(one, four), Add(Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = _neg_domain), Sum(index_or_indices = sub_expr1, summand = sub_expr2, 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[P_{\rm fail}\right]\left(e\right) \leq \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)

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