Expression of type NotEquals

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 ExprRange, Variable, m, n
from proveit.logic import NotEquals
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum import NumKet
from proveit.physics.quantum.QPE import _ket_u, _s, _t
from proveit.physics.quantum.circuits import MultiQubitElem, Output

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Interval(one, _t)
sub_expr3 = ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = Interval(Add(_t, one), Add(_t, _s))), one, _s)
expr = NotEquals([ExprRange(sub_expr1, MultiQubitElem(element = Output(state = NumKet(m, _t), part = sub_expr1), targets = sub_expr2), one, _t), sub_expr3], [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = NumKet(n, _t), part = sub_expr1), targets = sub_expr2), one, _t), sub_expr3])

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(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert m \rangle_{t}~\mbox{part}~1~\mbox{on}~\{1~\ldotp \ldotp~t\}} 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert m \rangle_{t}~\mbox{part}~2~\mbox{on}~\{1~\ldotp \ldotp~t\}} 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert m \rangle_{t}~\mbox{part}~t~\mbox{on}~\{1~\ldotp \ldotp~t\}} 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~1~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~2~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~s~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} 
} \end{array}\right) \neq \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert n \rangle_{t}~\mbox{part}~1~\mbox{on}~\{1~\ldotp \ldotp~t\}} 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert n \rangle_{t}~\mbox{part}~2~\mbox{on}~\{1~\ldotp \ldotp~t\}} 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert n \rangle_{t}~\mbox{part}~t~\mbox{on}~\{1~\ldotp \ldotp~t\}} 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~1~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~2~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~s~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} 
} \end{array}\right)

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	ExprTuple	5, 7
4	ExprTuple	6, 7
5	ExprRange	lambda_map: 8 start_index: 45 end_index: 46
6	ExprRange	lambda_map: 9 start_index: 45 end_index: 46
7	ExprRange	lambda_map: 10 start_index: 45 end_index: 47
8	Lambda	parameter: 34 body: 11
9	Lambda	parameter: 34 body: 12
10	Lambda	parameter: 34 body: 14
11	Operation	operator: 17 operands: 15
12	Operation	operator: 17 operands: 16
13	ExprTuple	34
14	Operation	operator: 17 operands: 18
15	NamedExprs	element: 19 targets: 21
16	NamedExprs	element: 20 targets: 21
17	Literal
18	NamedExprs	element: 22 targets: 23
19	Operation	operator: 27 operands: 24
20	Operation	operator: 27 operands: 25
21	Operation	operator: 29 operands: 26
22	Operation	operator: 27 operands: 28
23	Operation	operator: 29 operands: 30
24	NamedExprs	state: 31 part: 34
25	NamedExprs	state: 32 part: 34
26	ExprTuple	45, 46
27	Literal
28	NamedExprs	state: 33 part: 34
29	Literal
30	ExprTuple	35, 36
31	Operation	operator: 38 operands: 37
32	Operation	operator: 38 operands: 39
33	Literal
34	Variable
35	Operation	operator: 41 operands: 40
36	Operation	operator: 41 operands: 42
37	ExprTuple	43, 46
38	Literal
39	ExprTuple	44, 46
40	ExprTuple	46, 45
41	Literal
42	ExprTuple	46, 47
43	Variable
44	Variable
45	Literal
46	Literal
47	Literal