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), Or(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(\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)\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: 5 operands: 1
1	ExprTuple	2, 3
2	ExprRange	lambda_map: 4 start_index: 48 end_index: 49
3	Operation	operator: 5 operands: 6
4	Lambda	parameter: 42 body: 7
5	Literal
6	ExprTuple	8
7	Operation	operator: 17 operands: 9
8	ExprRange	lambda_map: 10 start_index: 48 end_index: 50
9	ExprTuple	11, 12
10	Lambda	parameter: 42 body: 14
11	Operation	operator: 26 operands: 15
12	Operation	operator: 26 operands: 16
13	ExprTuple	42
14	Operation	operator: 17 operands: 18
15	NamedExprs	element: 19 targets: 21
16	NamedExprs	element: 20 targets: 21
17	Literal
18	ExprTuple	22, 22
19	Operation	operator: 35 operands: 23
20	Operation	operator: 35 operands: 24
21	Operation	operator: 37 operands: 25
22	Operation	operator: 26 operands: 27
23	NamedExprs	state: 28 part: 42
24	NamedExprs	state: 29 part: 42
25	ExprTuple	48, 49
26	Literal
27	NamedExprs	element: 30 targets: 31
28	Operation	operator: 33 operands: 32
29	Operation	operator: 33 operands: 34
30	Operation	operator: 35 operands: 36
31	Operation	operator: 37 operands: 38
32	ExprTuple	39, 49
33	Literal
34	ExprTuple	40, 49
35	Literal
36	NamedExprs	state: 41 part: 42
37	Literal
38	ExprTuple	43, 44
39	Variable
40	Variable
41	Literal
42	Variable
43	Operation	operator: 46 operands: 45
44	Operation	operator: 46 operands: 47
45	ExprTuple	49, 48
46	Literal
47	ExprTuple	49, 50
48	Literal
49	Literal
50	Literal