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 Forall, InSet, NotEquals
from proveit.numbers import NaturalPos
from proveit.physics.quantum import NumKet
from proveit.physics.quantum.algebra import n_bit_interval

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [j, k], instance_expr = NotEquals(NumKet(j, n), NumKet(k, n)), domain = n_bit_interval, condition = NotEquals(j, k)), InSet(n, NaturalPos))

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\{\forall_{j, k \in \{0~\ldotp \ldotp~2^{n} - 1\}~|~j \neq k}~\left(\lvert j \rangle_{n} \neq \lvert k \rangle_{n}\right) \textrm{ if } n \in \mathbb{N}^+\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 operand: 6
2	Operation	operator: 23 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	43, 7
6	Lambda	parameters: 26 body: 8
7	Literal
8	Conditional	value: 9 condition: 10
9	Operation	operator: 25 operands: 11
10	Operation	operator: 12 operands: 13
11	ExprTuple	14, 15
12	Literal
13	ExprTuple	16, 17, 18
14	Operation	operator: 20 operands: 19
15	Operation	operator: 20 operands: 21
16	Operation	operator: 23 operands: 22
17	Operation	operator: 23 operands: 24
18	Operation	operator: 25 operands: 26
19	ExprTuple	28, 43
20	Literal
21	ExprTuple	29, 43
22	ExprTuple	28, 27
23	Literal
24	ExprTuple	29, 27
25	Literal
26	ExprTuple	28, 29
27	Operation	operator: 30 operands: 31
28	Variable
29	Variable
30	Literal
31	ExprTuple	32, 33
32	Literal
33	Operation	operator: 34 operands: 35
34	Literal
35	ExprTuple	36, 37
36	Operation	operator: 38 operands: 39
37	Operation	operator: 40 operand: 44
38	Literal
39	ExprTuple	42, 43
40	Literal
41	ExprTuple	44
42	Literal
43	Variable
44	Literal