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, Ceil, Log, Mult, frac, one, subtract, two
from proveit.physics.quantum.QPE import _eps, _n

# build up the expression from sub-expressions
sub_expr1 = Ceil(Log(two, Add(two, frac(one, Mult(two, _eps)))))
expr = Equals(subtract(Add(_n, sub_expr1), _n), sub_expr1)

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(\left(n + \left\lceil \textrm{log}_2\left(2 + \frac{1}{2 \cdot \epsilon}\right)\right\rceil\right) - n\right) = \left\lceil \textrm{log}_2\left(2 + \frac{1}{2 \cdot \epsilon}\right)\right\rceil

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