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
expr = Equals(subtract(Add(_n, Ceil(Log(two, Add(two, frac(one, Mult(two, _eps)))))), _n), Ceil(Log(two, Add(two, Mult(frac(one, two), Exp(_eps, Neg(one)))))))

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 + \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, 4
3	Operation	operator: 27 operands: 5
4	Operation	operator: 16 operand: 9
5	ExprTuple	7, 8
6	ExprTuple	9
7	Operation	operator: 27 operands: 10
8	Operation	operator: 36 operand: 14
9	Operation	operator: 21 operands: 12
10	ExprTuple	14, 13
11	ExprTuple	14
12	ExprTuple	42, 15
13	Operation	operator: 16 operand: 19
14	Literal
15	Operation	operator: 27 operands: 18
16	Literal
17	ExprTuple	19
18	ExprTuple	42, 20
19	Operation	operator: 21 operands: 22
20	Operation	operator: 40 operands: 23
21	Literal
22	ExprTuple	42, 24
23	ExprTuple	25, 26
24	Operation	operator: 27 operands: 28
25	Operation	operator: 34 operands: 29
26	Operation	operator: 30 operands: 31
27	Literal
28	ExprTuple	42, 32
29	ExprTuple	39, 42
30	Literal
31	ExprTuple	43, 33
32	Operation	operator: 34 operands: 35
33	Operation	operator: 36 operand: 39
34	Literal
35	ExprTuple	39, 38
36	Literal
37	ExprTuple	39
38	Operation	operator: 40 operands: 41
39	Literal
40	Literal
41	ExprTuple	42, 43
42	Literal
43	Literal