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, _pos_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 = _pos_domain), Sum(index_or_indices = sub_expr1, summand = frac(one, Mult(four, Exp(_diff_l_scaled_delta_floor, 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(\sum_{l = e + 1}^{2^{t - 1}} \left|\alpha_{b_{\textit{f}} \oplus l}\right|^{2}\right) \leq \left(\sum_{l = e + 1}^{2^{t - 1}} \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: 60 operands: 16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operands: 20
16	ExprTuple	21, 64
17	Literal
18	ExprTuple	55, 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: 60 operands: 36
32	Operation	operator: 46 operands: 37
33	Operation	operator: 60 operands: 38
34	Literal
35	ExprTuple	39
36	ExprTuple	40, 64
37	ExprTuple	41, 55
38	ExprTuple	64, 42
39	Operation	operator: 43 operands: 44
40	Operation	operator: 46 operands: 45
41	Variable
42	Operation	operator: 46 operands: 47
43	Literal
44	ExprTuple	66, 48
45	ExprTuple	48, 49
46	Literal
47	ExprTuple	65, 50
48	Variable
49	Operation	operator: 52 operand: 54
50	Operation	operator: 52 operand: 55
51	ExprTuple	54
52	Literal
53	ExprTuple	55
54	Operation	operator: 56 operands: 57
55	Literal
56	Literal
57	ExprTuple	58, 59
58	Operation	operator: 60 operands: 61
59	Operation	operator: 62 operand: 66
60	Literal
61	ExprTuple	64, 65
62	Literal
63	ExprTuple	66
64	Literal
65	Literal
66	Literal