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)
sub_expr3 = frac(sub_expr1, sub_expr2)
sub_expr4 = frac(one, sub_expr2)
expr = Equals(subtract(Neg(sub_expr3), sub_expr4), Neg(Add(sub_expr3, sub_expr4)))

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{2 + \frac{1}{\epsilon}}{\left(2 + \frac{1}{\epsilon}\right)^{2}} - \frac{1}{\left(2 + \frac{1}{\epsilon}\right)^{2}}\right) = \left(-\left(\frac{2 + \frac{1}{\epsilon}}{\left(2 + \frac{1}{\epsilon}\right)^{2}} + \frac{1}{\left(2 + \frac{1}{\epsilon}\right)^{2}}\right)\right)

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: 22 operands: 5
4	Operation	operator: 11 operand: 9
5	ExprTuple	7, 8
6	ExprTuple	9
7	Operation	operator: 11 operand: 14
8	Operation	operator: 11 operand: 15
9	Operation	operator: 22 operands: 13
10	ExprTuple	14
11	Literal
12	ExprTuple	15
13	ExprTuple	14, 15
14	Operation	operator: 26 operands: 16
15	Operation	operator: 26 operands: 17
16	ExprTuple	21, 18
17	ExprTuple	28, 18
18	Operation	operator: 19 operands: 20
19	Literal
20	ExprTuple	21, 24
21	Operation	operator: 22 operands: 23
22	Literal
23	ExprTuple	24, 25
24	Literal
25	Operation	operator: 26 operands: 27
26	Literal
27	ExprTuple	28, 29
28	Literal
29	Literal