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, 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(Add(_n, sub_expr1, Neg(_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(n + \left\lceil \textrm{log}_2\left(2 + \left(\frac{1}{2} \cdot \epsilon^{-1}\right)\right)\right\rceil - n\right) = \left\lceil \textrm{log}_2\left(2 + \left(\frac{1}{2} \cdot \epsilon^{-1}\right)\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, 5
3	Operation	operator: 15 operands: 4
4	ExprTuple	11, 5, 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 29 operand: 11
7	Literal
8	ExprTuple	10
9	ExprTuple	11
10	Operation	operator: 12 operands: 13
11	Literal
12	Literal
13	ExprTuple	26, 14
14	Operation	operator: 15 operands: 16
15	Literal
16	ExprTuple	26, 17
17	Operation	operator: 18 operands: 19
18	Literal
19	ExprTuple	20, 21
20	Operation	operator: 22 operands: 23
21	Operation	operator: 24 operands: 25
22	Literal
23	ExprTuple	31, 26
24	Literal
25	ExprTuple	27, 28
26	Literal
27	Literal
28	Operation	operator: 29 operand: 31
29	Literal
30	ExprTuple	31
31	Literal