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 TensorProd
from proveit.logic import Equals, InSet
from proveit.numbers import Add, Exp, one, two
from proveit.physics.quantum import NumKet, ket1
from proveit.physics.quantum.algebra import n_bit_interval

# build up the expression from sub-expressions
expr = Conditional(Equals(NumKet(Add(Exp(two, n), k), Add(n, one)), TensorProd(ket1, NumKet(k, n))), 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\{\lvert 2^{n} + k \rangle_{n + 1} = \left(\lvert 1 \rangle {\otimes} \lvert k \rangle_{n}\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: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	28, 9
7	Operation	operator: 24 operands: 10
8	Operation	operator: 11 operands: 12
9	Operation	operator: 13 operands: 14
10	ExprTuple	15, 16
11	Literal
12	ExprTuple	17, 18
13	Literal
14	ExprTuple	19, 20
15	Operation	operator: 26 operands: 21
16	Operation	operator: 26 operands: 22
17	Operation	operator: 23 operand: 37
18	Operation	operator: 24 operands: 25
19	Literal
20	Operation	operator: 26 operands: 27
21	ExprTuple	29, 28
22	ExprTuple	36, 37
23	Literal
24	Literal
25	ExprTuple	28, 36
26	Literal
27	ExprTuple	29, 30
28	Variable
29	Operation	operator: 31 operands: 32
30	Operation	operator: 33 operand: 37
31	Literal
32	ExprTuple	35, 36
33	Literal
34	ExprTuple	37
35	Literal
36	Variable
37	Literal