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, Neg, frac, one, subtract, two
from proveit.physics.quantum.QPE import _eps

# build up the expression from sub-expressions
sub_expr1 = Add(two, frac(one, _eps))
sub_expr2 = Exp(sub_expr1, two)
expr = Equals(Add(one, Neg(frac(sub_expr1, sub_expr2)), Neg(frac(one, sub_expr2))), subtract(one, frac(Add(sub_expr1, one), 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 - \frac{2 + \frac{1}{\epsilon}}{\left(2 + \frac{1}{\epsilon}\right)^{2}} - \frac{1}{\left(2 + \frac{1}{\epsilon}\right)^{2}}\right) =  \\ \left(1 - \frac{\left(2 + \frac{1}{\epsilon}\right) + 1}{\left(2 + \frac{1}{\epsilon}\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: 26 operands: 5
4	Operation	operator: 26 operands: 6
5	ExprTuple	32, 7, 8
6	ExprTuple	32, 9
7	Operation	operator: 12 operand: 14
8	Operation	operator: 12 operand: 15
9	Operation	operator: 12 operand: 16
10	ExprTuple	14
11	ExprTuple	15
12	Literal
13	ExprTuple	16
14	Operation	operator: 30 operands: 17
15	Operation	operator: 30 operands: 18
16	Operation	operator: 30 operands: 19
17	ExprTuple	25, 21
18	ExprTuple	32, 21
19	ExprTuple	20, 21
20	Operation	operator: 26 operands: 22
21	Operation	operator: 23 operands: 24
22	ExprTuple	25, 32
23	Literal
24	ExprTuple	25, 28
25	Operation	operator: 26 operands: 27
26	Literal
27	ExprTuple	28, 29
28	Literal
29	Operation	operator: 30 operands: 31
30	Literal
31	ExprTuple	32, 33
32	Literal
33	Literal