Expression of type Len

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 Lambda, Variable, m
from proveit.core_expr_types import Len
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}")
expr = Len(operands = [Lambda(sub_expr1, MultiQubitElem(element = Output(state = NumKet(m, _t), part = sub_expr1), targets = Interval(one, _t))), Lambda(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = Interval(Add(_t, one), Add(_t, _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({_{-}a} \mapsto \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert m \rangle_{t}~\mbox{part}~{_{-}a}~\mbox{on}~\{1~\ldotp \ldotp~t\}} 
} \end{array}, {_{-}a} \mapsto \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~{_{-}a}~\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	Lambda	parameter: 23 body: 5
4	Lambda	parameter: 23 body: 7
5	Operation	operator: 9 operands: 8
6	ExprTuple	23
7	Operation	operator: 9 operands: 10
8	NamedExprs	element: 11 targets: 12
9	Literal
10	NamedExprs	element: 13 targets: 14
11	Operation	operator: 17 operands: 15
12	Operation	operator: 19 operands: 16
13	Operation	operator: 17 operands: 18
14	Operation	operator: 19 operands: 20
15	NamedExprs	state: 21 part: 23
16	ExprTuple	32, 33
17	Literal
18	NamedExprs	state: 22 part: 23
19	Literal
20	ExprTuple	24, 25
21	Operation	operator: 26 operands: 27
22	Literal
23	Variable
24	Operation	operator: 29 operands: 28
25	Operation	operator: 29 operands: 30
26	Literal
27	ExprTuple	31, 33
28	ExprTuple	33, 32
29	Literal
30	ExprTuple	33, 34
31	Variable
32	Literal
33	Literal
34	Literal