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, j, k, n
from proveit.logic import And, InSet, NotEquals
from proveit.physics.quantum import NumKet
from proveit.physics.quantum.algebra import n_bit_interval

# build up the expression from sub-expressions
expr = Conditional(NotEquals(NumKet(j, n), NumKet(k, n)), And(InSet(j, n_bit_interval), InSet(k, n_bit_interval), NotEquals(j, k)))

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 j \rangle_{n} \neq \lvert k \rangle_{n} \textrm{ if } j \in \{0~\ldotp \ldotp~2^{n} - 1\} ,  k \in \{0~\ldotp \ldotp~2^{n} - 1\} ,  j \neq k\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: 17 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	8, 9, 10
6	Operation	operator: 12 operands: 11
7	Operation	operator: 12 operands: 13
8	Operation	operator: 15 operands: 14
9	Operation	operator: 15 operands: 16
10	Operation	operator: 17 operands: 18
11	ExprTuple	20, 35
12	Literal
13	ExprTuple	21, 35
14	ExprTuple	20, 19
15	Literal
16	ExprTuple	21, 19
17	Literal
18	ExprTuple	20, 21
19	Operation	operator: 22 operands: 23
20	Variable
21	Variable
22	Literal
23	ExprTuple	24, 25
24	Literal
25	Operation	operator: 26 operands: 27
26	Literal
27	ExprTuple	28, 29
28	Operation	operator: 30 operands: 31
29	Operation	operator: 32 operand: 36
30	Literal
31	ExprTuple	34, 35
32	Literal
33	ExprTuple	36
34	Literal
35	Variable
36	Literal