Expression of type Equals

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 Equals
from proveit.numbers import Add, Exp, Mult, Neg, four, frac, one, subtract, two
from proveit.physics.quantum.QPE import _e_value

# build up the expression from sub-expressions
sub_expr1 = Neg(frac(one, Mult(two, _e_value)))
sub_expr2 = frac(one, Mult(four, Exp(_e_value, two)))
expr = Equals(Add(one, subtract(sub_expr1, sub_expr2)), Add(one, sub_expr1, Neg(sub_expr2))).with_wrapping_at(2)

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())

\begin{array}{c} \begin{array}{l} \left(1 + \left(-\frac{1}{2 \cdot \left(2^{t - n} - 1\right)} - \frac{1}{4 \cdot \left(2^{t - n} - 1\right)^{2}}\right)\right) =  \\ \left(1 - \frac{1}{2 \cdot \left(2^{t - n} - 1\right)} - \frac{1}{4 \cdot \left(2^{t - n} - 1\right)^{2}}\right) \end{array} \end{array}

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.	()	(2)	('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: 36 operands: 5
4	Operation	operator: 36 operands: 6
5	ExprTuple	35, 7
6	ExprTuple	35, 9, 10
7	Operation	operator: 36 operands: 8
8	ExprTuple	9, 10
9	Operation	operator: 40 operand: 13
10	Operation	operator: 40 operand: 14
11	ExprTuple	13
12	ExprTuple	14
13	Operation	operator: 16 operands: 15
14	Operation	operator: 16 operands: 17
15	ExprTuple	35, 18
16	Literal
17	ExprTuple	35, 19
18	Operation	operator: 21 operands: 20
19	Operation	operator: 21 operands: 22
20	ExprTuple	33, 26
21	Literal
22	ExprTuple	23, 24
23	Literal
24	Operation	operator: 30 operands: 25
25	ExprTuple	26, 33
26	Operation	operator: 36 operands: 27
27	ExprTuple	28, 29
28	Operation	operator: 30 operands: 31
29	Operation	operator: 40 operand: 35
30	Literal
31	ExprTuple	33, 34
32	ExprTuple	35
33	Literal
34	Operation	operator: 36 operands: 37
35	Literal
36	Literal
37	ExprTuple	38, 39
38	Literal
39	Operation	operator: 40 operand: 42
40	Literal
41	ExprTuple	42
42	Literal