Expression of type Conditional

from the theory of proveit.physics.quantum.algebra

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 Conditional, k, n
from proveit.linear_algebra import LinMap
from proveit.logic import CartExp, InSet
from proveit.numbers import Complex, Exp, two
from proveit.physics.quantum import NumBra
from proveit.physics.quantum.algebra import n_bit_interval

# build up the expression from sub-expressions
expr = Conditional(InSet(NumBra(k, n), LinMap(CartExp(Complex, Exp(two, n)), Complex)), InSet(k, n_bit_interval))

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\{{_{n}}\langle k \rvert \in \mathcal{L}\left(\mathbb{C}^{2^{n}}, \mathbb{C}\right) \textrm{ if } k \in \{0~\ldotp \ldotp~2^{n} - 1\}\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 4 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	15, 8
6	Operation	operator: 9 operands: 10
7	Operation	operator: 11 operands: 12
8	Operation	operator: 13 operands: 14
9	Literal
10	ExprTuple	15, 31
11	Literal
12	ExprTuple	16, 23
13	Literal
14	ExprTuple	17, 18
15	Variable
16	Operation	operator: 19 operands: 20
17	Literal
18	Operation	operator: 21 operands: 22
19	Literal
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	24, 25
23	Literal
24	Operation	operator: 26 operands: 27
25	Operation	operator: 28 operand: 32
26	Literal
27	ExprTuple	30, 31
28	Literal
29	ExprTuple	32
30	Literal
31	Variable
32	Literal