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 Exp, Integrate, IntervalCC, LessEq, frac, one, subtract, two
from proveit.physics.quantum.QPE import _two_pow__t_minus_one

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

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(\int_{e}^{2^{t - 1} - 1} \frac{1}{l^{2}}\,dl\right) \leq \frac{1}{e}

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: 8
4	Operation	operator: 13 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	37, 23
8	Lambda	parameter: 22 body: 10
9	ExprTuple	22
10	Conditional	value: 11 condition: 12
11	Operation	operator: 13 operands: 14
12	Operation	operator: 15 operands: 16
13	Literal
14	ExprTuple	37, 17
15	Literal
16	ExprTuple	22, 18
17	Operation	operator: 27 operands: 19
18	Operation	operator: 20 operands: 21
19	ExprTuple	22, 29
20	Literal
21	ExprTuple	23, 24
22	Variable
23	Variable
24	Operation	operator: 31 operands: 25
25	ExprTuple	26, 34
26	Operation	operator: 27 operands: 28
27	Literal
28	ExprTuple	29, 30
29	Literal
30	Operation	operator: 31 operands: 32
31	Literal
32	ExprTuple	33, 34
33	Literal
34	Operation	operator: 35 operand: 37
35	Literal
36	ExprTuple	37
37	Literal