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 import Variable
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(subtract(Neg(frac(sub_expr1, sub_expr2)), frac(one, sub_expr2)), Variable("_a", latex_format = r"{_{-}a}"))

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) = {_{-}a}

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