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 Abs, Exp, LessEq, Mult, Sum, four, frac, one, two
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _neg_domain, _rel_indexed_alpha

# build up the expression from sub-expressions
sub_expr1 = [l]
expr = LessEq(Sum(index_or_indices = sub_expr1, summand = Exp(Abs(_rel_indexed_alpha), two), domain = _neg_domain), Sum(index_or_indices = sub_expr1, summand = frac(one, Mult(four, Exp(_diff_l_scaled_delta_floor, two))), domain = _neg_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(\sum_{l = -2^{t - 1} + 1}^{-\left(e + 1\right)} \left|\alpha_{b_{\textit{f}} \oplus l}\right|^{2}\right) \leq \left(\sum_{l = -2^{t - 1} + 1}^{-\left(e + 1\right)} \frac{1}{4 \cdot \left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}\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: 6 operand: 8
4	Operation	operator: 6 operand: 9
5	ExprTuple	8
6	Literal
7	ExprTuple	9
8	Lambda	parameter: 48 body: 10
9	Lambda	parameter: 48 body: 12
10	Conditional	value: 13 condition: 15
11	ExprTuple	48
12	Conditional	value: 14 condition: 15
13	Operation	operator: 63 operands: 16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operands: 20
16	ExprTuple	21, 69
17	Literal
18	ExprTuple	72, 22
19	Literal
20	ExprTuple	48, 23
21	Operation	operator: 24 operand: 29
22	Operation	operator: 56 operands: 26
23	Operation	operator: 27 operands: 28
24	Literal
25	ExprTuple	29
26	ExprTuple	30, 31
27	Literal
28	ExprTuple	32, 33
29	Operation	operator: 34 operand: 39
30	Literal
31	Operation	operator: 63 operands: 36
32	Operation	operator: 58 operands: 37
33	Operation	operator: 67 operand: 42
34	Literal
35	ExprTuple	39
36	ExprTuple	40, 69
37	ExprTuple	41, 72
38	ExprTuple	42
39	Operation	operator: 43 operands: 44
40	Operation	operator: 58 operands: 45
41	Operation	operator: 67 operand: 50
42	Operation	operator: 58 operands: 47
43	Literal
44	ExprTuple	71, 48
45	ExprTuple	48, 49
46	ExprTuple	50
47	ExprTuple	51, 72
48	Variable
49	Operation	operator: 67 operand: 54
50	Operation	operator: 63 operands: 53
51	Variable
52	ExprTuple	54
53	ExprTuple	69, 55
54	Operation	operator: 56 operands: 57
55	Operation	operator: 58 operands: 59
56	Literal
57	ExprTuple	60, 61
58	Literal
59	ExprTuple	70, 62
60	Operation	operator: 63 operands: 64
61	Operation	operator: 65 operand: 71
62	Operation	operator: 67 operand: 72
63	Literal
64	ExprTuple	69, 70
65	Literal
66	ExprTuple	71
67	Literal
68	ExprTuple	72
69	Literal
70	Literal
71	Literal
72	Literal