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, Exp, Log, Mult, Neg, 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, Mult(frac(one, two), Exp(_eps, Neg(one))))))
expr = Equals(subtract(Add(_n, sub_expr1), _n), Add(_n, sub_expr1, Neg(_n))).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(\left(n + \left\lceil \textrm{log}_2\left(2 + \left(\frac{1}{2} \cdot \epsilon^{-1}\right)\right)\right\rceil\right) - n\right) =  \\ \left(n + \left\lceil \textrm{log}_2\left(2 + \left(\frac{1}{2} \cdot \epsilon^{-1}\right)\right)\right\rceil - n\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: 19 operands: 5
4	Operation	operator: 19 operands: 6
5	ExprTuple	7, 8
6	ExprTuple	12, 11, 8
7	Operation	operator: 19 operands: 9
8	Operation	operator: 33 operand: 12
9	ExprTuple	12, 11
10	ExprTuple	12
11	Operation	operator: 13 operand: 15
12	Literal
13	Literal
14	ExprTuple	15
15	Operation	operator: 16 operands: 17
16	Literal
17	ExprTuple	30, 18
18	Operation	operator: 19 operands: 20
19	Literal
20	ExprTuple	30, 21
21	Operation	operator: 22 operands: 23
22	Literal
23	ExprTuple	24, 25
24	Operation	operator: 26 operands: 27
25	Operation	operator: 28 operands: 29
26	Literal
27	ExprTuple	35, 30
28	Literal
29	ExprTuple	31, 32
30	Literal
31	Literal
32	Operation	operator: 33 operand: 35
33	Literal
34	ExprTuple	35
35	Literal