Expression of type Or

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, Or
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 = MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = Interval(Add(_t, one), Add(_t, _s)))
expr = Or(ExprRange(sub_expr1, NotEquals(MultiQubitElem(element = Output(state = NumKet(m, _t), part = sub_expr1), targets = sub_expr2), MultiQubitElem(element = Output(state = NumKet(n, _t), part = sub_expr1), targets = sub_expr2)), one, _t), ExprRange(sub_expr1, NotEquals(sub_expr3, sub_expr3), one, _s))

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} \neq \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert n \rangle_{t}~\mbox{part}~1~\mbox{on}~\{1~\ldotp \ldotp~t\}} 
} \end{array}\right) \lor  \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert m \rangle_{t}~\mbox{part}~2~\mbox{on}~\{1~\ldotp \ldotp~t\}} 
} \end{array} \neq \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert n \rangle_{t}~\mbox{part}~2~\mbox{on}~\{1~\ldotp \ldotp~t\}} 
} \end{array}\right) \lor  \ldots \lor  \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert m \rangle_{t}~\mbox{part}~t~\mbox{on}~\{1~\ldotp \ldotp~t\}} 
} \end{array} \neq \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert n \rangle_{t}~\mbox{part}~t~\mbox{on}~\{1~\ldotp \ldotp~t\}} 
} \end{array}\right)\lor \left(\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} \neq \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}\right) \lor  \left(\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} \neq \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}\right) \lor  \ldots \lor  \left(\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} \neq \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',)

# 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	ExprRange	lambda_map: 5 start_index: 46 end_index: 47
4	ExprRange	lambda_map: 6 start_index: 46 end_index: 48
5	Lambda	parameter: 35 body: 7
6	Lambda	parameter: 35 body: 9
7	Operation	operator: 11 operands: 10
8	ExprTuple	35
9	Operation	operator: 11 operands: 12
10	ExprTuple	13, 14
11	Literal
12	ExprTuple	15, 15
13	Operation	operator: 18 operands: 16
14	Operation	operator: 18 operands: 17
15	Operation	operator: 18 operands: 19
16	NamedExprs	element: 20 targets: 22
17	NamedExprs	element: 21 targets: 22
18	Literal
19	NamedExprs	element: 23 targets: 24
20	Operation	operator: 28 operands: 25
21	Operation	operator: 28 operands: 26
22	Operation	operator: 30 operands: 27
23	Operation	operator: 28 operands: 29
24	Operation	operator: 30 operands: 31
25	NamedExprs	state: 32 part: 35
26	NamedExprs	state: 33 part: 35
27	ExprTuple	46, 47
28	Literal
29	NamedExprs	state: 34 part: 35
30	Literal
31	ExprTuple	36, 37
32	Operation	operator: 39 operands: 38
33	Operation	operator: 39 operands: 40
34	Literal
35	Variable
36	Operation	operator: 42 operands: 41
37	Operation	operator: 42 operands: 43
38	ExprTuple	44, 47
39	Literal
40	ExprTuple	45, 47
41	ExprTuple	47, 46
42	Literal
43	ExprTuple	47, 48
44	Variable
45	Variable
46	Literal
47	Literal
48	Literal