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, x
from proveit.numbers import Add, Exp, Integrate, Interval, IntervalCC, LessEq, Sum, frac, one, subtract, two
from proveit.physics.quantum.QPE import _two_pow__t_minus_one

# build up the expression from sub-expressions
sub_expr1 = subtract(_two_pow__t_minus_one, one)
expr = LessEq(Sum(index_or_indices = [l], summand = frac(one, Exp(l, two)), domain = Interval(Add(e, one), sub_expr1)), Integrate(index_or_indices = [x], integrand = frac(one, Exp(x, two)), domain = IntervalCC(e, sub_expr1)))

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} - 1} \frac{1}{l^{2}}\right) \leq \left(\int_{e}^{2^{t - 1} - 1} \frac{1}{x^{2}}\,dx\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: 9
4	Operation	operator: 7 operand: 10
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	10
9	Lambda	parameter: 35 body: 12
10	Lambda	parameter: 37 body: 14
11	ExprTuple	35
12	Conditional	value: 15 condition: 16
13	ExprTuple	37
14	Conditional	value: 17 condition: 18
15	Operation	operator: 21 operands: 19
16	Operation	operator: 23 operands: 20
17	Operation	operator: 21 operands: 22
18	Operation	operator: 23 operands: 24
19	ExprTuple	53, 25
20	ExprTuple	35, 26
21	Literal
22	ExprTuple	53, 27
23	Literal
24	ExprTuple	37, 28
25	Operation	operator: 43 operands: 29
26	Operation	operator: 30 operands: 31
27	Operation	operator: 43 operands: 32
28	Operation	operator: 33 operands: 34
29	ExprTuple	35, 45
30	Literal
31	ExprTuple	36, 38
32	ExprTuple	37, 45
33	Literal
34	ExprTuple	41, 38
35	Variable
36	Operation	operator: 47 operands: 39
37	Variable
38	Operation	operator: 47 operands: 40
39	ExprTuple	41, 53
40	ExprTuple	42, 50
41	Variable
42	Operation	operator: 43 operands: 44
43	Literal
44	ExprTuple	45, 46
45	Literal
46	Operation	operator: 47 operands: 48
47	Literal
48	ExprTuple	49, 50
49	Literal
50	Operation	operator: 51 operand: 53
51	Literal
52	ExprTuple	53
53	Literal