Expression of type ExprTuple

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, ExprTuple, Lambda, 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 = ExprTuple(Lambda(n, 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(n \mapsto \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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 46 body: 3
2	ExprTuple	46
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 26 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	46, 10
9	Lambda	parameters: 29 body: 11
10	Literal
11	Conditional	value: 12 condition: 13
12	Operation	operator: 28 operands: 14
13	Operation	operator: 15 operands: 16
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	19, 20, 21
17	Operation	operator: 23 operands: 22
18	Operation	operator: 23 operands: 24
19	Operation	operator: 26 operands: 25
20	Operation	operator: 26 operands: 27
21	Operation	operator: 28 operands: 29
22	ExprTuple	31, 46
23	Literal
24	ExprTuple	32, 46
25	ExprTuple	31, 30
26	Literal
27	ExprTuple	32, 30
28	Literal
29	ExprTuple	31, 32
30	Operation	operator: 33 operands: 34
31	Variable
32	Variable
33	Literal
34	ExprTuple	35, 36
35	Literal
36	Operation	operator: 37 operands: 38
37	Literal
38	ExprTuple	39, 40
39	Operation	operator: 41 operands: 42
40	Operation	operator: 43 operand: 47
41	Literal
42	ExprTuple	45, 46
43	Literal
44	ExprTuple	47
45	Literal
46	Variable
47	Literal