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 A, B, C, D, ExprRange, ExprTuple, Function, IndexedVar, Q, Variable, alpha, beta, c, delta, gamma, j, m, n
from proveit.core_expr_types import Q__b_1_to_j, b_1_to_j, f__b_1_to_j
from proveit.linear_algebra import MatrixSpace
from proveit.logic import CartExp, Forall, InSet
from proveit.numbers import Complex, NaturalPos, one
from proveit.physics.quantum import ket_psi, ket_varphi

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = MatrixSpace(field = Complex, rows = n, columns = m)
expr = ExprTuple(InSet(alpha, Complex), InSet(beta, Complex), InSet(gamma, Complex), InSet(delta, Complex), InSet(j, NaturalPos), InSet(m, NaturalPos), InSet(n, NaturalPos), InSet(ket_psi, CartExp(Complex, m)), InSet(A, sub_expr2), InSet(B, sub_expr2), InSet(C, sub_expr2), InSet(D, MatrixSpace(field = Complex, rows = m, columns = n)), InSet(ket_varphi, CartExp(Complex, n)), Forall(instance_param_or_params = [b_1_to_j], instance_expr = InSet(f__b_1_to_j, sub_expr2), condition = Q__b_1_to_j), Function(Q, [ExprRange(sub_expr1, IndexedVar(c, sub_expr1), one, j)]))

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(\alpha \in \mathbb{C}, \beta \in \mathbb{C}, \gamma \in \mathbb{C}, \delta \in \mathbb{C}, j \in \mathbb{N}^+, m \in \mathbb{N}^+, n \in \mathbb{N}^+, \lvert \psi \rangle \in \mathbb{C}^{m}, A \in \mathbb{C}^{n \times m}, B \in \mathbb{C}^{n \times m}, C \in \mathbb{C}^{n \times m}, D \in \mathbb{C}^{m \times n}, \lvert \varphi \rangle \in \mathbb{C}^{n}, \forall_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~\left(f\left(b_{1}, b_{2}, \ldots, b_{j}\right) \in \mathbb{C}^{n \times m}\right), Q\left(c_{1}, c_{2}, \ldots, c_{j}\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15
1	Operation	operator: 62 operands: 16
2	Operation	operator: 62 operands: 17
3	Operation	operator: 62 operands: 18
4	Operation	operator: 62 operands: 19
5	Operation	operator: 62 operands: 20
6	Operation	operator: 62 operands: 21
7	Operation	operator: 62 operands: 22
8	Operation	operator: 62 operands: 23
9	Operation	operator: 62 operands: 24
10	Operation	operator: 62 operands: 25
11	Operation	operator: 62 operands: 26
12	Operation	operator: 62 operands: 27
13	Operation	operator: 62 operands: 28
14	Operation	operator: 29 operand: 46
15	Operation	operator: 64 operands: 31
16	ExprTuple	32, 73
17	ExprTuple	33, 73
18	ExprTuple	34, 73
19	ExprTuple	35, 73
20	ExprTuple	78, 36
21	ExprTuple	75, 36
22	ExprTuple	74, 36
23	ExprTuple	37, 38
24	ExprTuple	39, 67
25	ExprTuple	40, 67
26	ExprTuple	41, 67
27	ExprTuple	42, 43
28	ExprTuple	44, 45
29	Literal
30	ExprTuple	46
31	ExprTuple	47
32	Variable
33	Variable
34	Variable
35	Variable
36	Literal
37	Operation	operator: 51 operand: 57
38	Operation	operator: 53 operands: 49
39	Variable
40	Variable
41	Variable
42	Variable
43	Operation	operator: 70 operands: 50
44	Operation	operator: 51 operand: 58
45	Operation	operator: 53 operands: 54
46	Lambda	parameters: 69 body: 55
47	ExprRange	lambda_map: 56 start_index: 77 end_index: 78
48	ExprTuple	57
49	ExprTuple	73, 75
50	NamedExprs	field: 73 rows: 75 columns: 74
51	Literal
52	ExprTuple	58
53	Literal
54	ExprTuple	73, 74
55	Conditional	value: 59 condition: 60
56	Lambda	parameter: 82 body: 61
57	Variable
58	Variable
59	Operation	operator: 62 operands: 63
60	Operation	operator: 64 operands: 69
61	IndexedVar	variable: 65 index: 82
62	Literal
63	ExprTuple	66, 67
64	Variable
65	Variable
66	Operation	operator: 68 operands: 69
67	Operation	operator: 70 operands: 71
68	Variable
69	ExprTuple	72
70	Literal
71	NamedExprs	field: 73 rows: 74 columns: 75
72	ExprRange	lambda_map: 76 start_index: 77 end_index: 78
73	Literal
74	Variable
75	Variable
76	Lambda	parameter: 82 body: 79
77	Literal
78	Variable
79	IndexedVar	variable: 80 index: 82
80	Variable
81	ExprTuple	82
82	Variable