Expression of type InSet

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.logic import InSet
from proveit.numbers import Exp, Mult, Neg, Real, four, frac, one, subtract, two
from proveit.physics.quantum.QPE import _e_value

# build up the expression from sub-expressions
expr = InSet(subtract(Neg(frac(one, Mult(two, _e_value))), frac(one, Mult(four, Exp(_e_value, two)))), Real)

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(-\frac{1}{2 \cdot \left(2^{t - n} - 1\right)} - \frac{1}{4 \cdot \left(2^{t - n} - 1\right)^{2}}\right) \in \mathbb{R}

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: 33 operands: 5
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 37 operand: 10
7	Operation	operator: 37 operand: 11
8	ExprTuple	10
9	ExprTuple	11
10	Operation	operator: 13 operands: 12
11	Operation	operator: 13 operands: 14
12	ExprTuple	32, 15
13	Literal
14	ExprTuple	32, 16
15	Operation	operator: 18 operands: 17
16	Operation	operator: 18 operands: 19
17	ExprTuple	30, 23
18	Literal
19	ExprTuple	20, 21
20	Literal
21	Operation	operator: 27 operands: 22
22	ExprTuple	23, 30
23	Operation	operator: 33 operands: 24
24	ExprTuple	25, 26
25	Operation	operator: 27 operands: 28
26	Operation	operator: 37 operand: 32
27	Literal
28	ExprTuple	30, 31
29	ExprTuple	32
30	Literal
31	Operation	operator: 33 operands: 34
32	Literal
33	Literal
34	ExprTuple	35, 36
35	Literal
36	Operation	operator: 37 operand: 39
37	Literal
38	ExprTuple	39
39	Literal