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 Add, Exp, Mult, Real, four, frac, one, two
from proveit.physics.quantum.QPE import _e_value

# build up the expression from sub-expressions
expr = InSet(Add(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: 29 operands: 5
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 9 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	28, 11
9	Literal
10	ExprTuple	28, 12
11	Operation	operator: 14 operands: 13
12	Operation	operator: 14 operands: 15
13	ExprTuple	26, 19
14	Literal
15	ExprTuple	16, 17
16	Literal
17	Operation	operator: 23 operands: 18
18	ExprTuple	19, 26
19	Operation	operator: 29 operands: 20
20	ExprTuple	21, 22
21	Operation	operator: 23 operands: 24
22	Operation	operator: 33 operand: 28
23	Literal
24	ExprTuple	26, 27
25	ExprTuple	28
26	Literal
27	Operation	operator: 29 operands: 30
28	Literal
29	Literal
30	ExprTuple	31, 32
31	Literal
32	Operation	operator: 33 operand: 35
33	Literal
34	ExprTuple	35
35	Literal