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 import ExprRange, Variable, t
from proveit.linear_algebra import TensorProd
from proveit.logic import Equals
from proveit.numbers import Add, Interval, Neg, one, two, zero
from proveit.physics.quantum.QPE import _ket_u, _psi_t_ket, _s
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 = Neg(t)
sub_expr3 = TensorProd(_psi_t_ket, _ket_u)
sub_expr4 = Interval(one, Add(t, _s))
sub_expr5 = MultiQubitElem(element = Output(state = sub_expr3, part = Add(sub_expr1, t)), targets = sub_expr4)
expr = Equals([MultiQubitElem(element = Output(state = sub_expr3, part = one), targets = sub_expr4), ExprRange(sub_expr1, sub_expr5, Add(sub_expr2, two), zero)], [ExprRange(sub_expr1, sub_expr5, Add(sub_expr2, one), zero)]).with_wrapping_at(2)

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())

\begin{array}{c} \begin{array}{l} \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~1~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~\left(-t + 2\right) + t~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~\left(-t + 3\right) + t~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~0 + t~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \end{array}\right) =  \\ \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~\left(-t + 1\right) + t~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~\left(-t + 2\right) + t~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~0 + t~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \end{array}\right) \end{array} \end{array}

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