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, Conditional, ExprTuple, Lambda, i, n
from proveit.core_expr_types import a_1_to_n, a_i, b_1_to_n, b_i, v_1_to_n, v_i
from proveit.linear_algebra import OrthoNormBases, ScalarMult, VecSum
from proveit.logic import And, CartExp, Equals, Exists, InSet, Set
from proveit.numbers import Complex, Interval, one
from proveit.physics.quantum import Bra, Ket, Qmult

# build up the expression from sub-expressions
sub_expr1 = [i]
sub_expr2 = Interval(one, n)
sub_expr3 = Qmult(Ket(v_i), Bra(v_i))
expr = ExprTuple(Lambda([v_1_to_n], Conditional(Exists(instance_param_or_params = [a_1_to_n, b_1_to_n], instance_expr = And(Equals(A, VecSum(index_or_indices = sub_expr1, summand = ScalarMult(a_i, sub_expr3), domain = sub_expr2)), Equals(B, VecSum(index_or_indices = sub_expr1, summand = ScalarMult(b_i, sub_expr3), domain = sub_expr2))).with_wrapping_at(2), domain = Complex).with_wrapping(), InSet(Set(v_1_to_n), OrthoNormBases(CartExp(Complex, n))))))

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(\left(v_{1}, v_{2}, \ldots, v_{n}\right) \mapsto \left\{\begin{array}{l}\exists_{a_{1}, a_{2}, \ldots, a_{n}, b_{1}, b_{2}, \ldots, b_{n} \in \mathbb{C}}~\\
\left(\begin{array}{c} \left(A = \left(\sum_{i=1}^{n} \left(a_{i} \cdot \left(\lvert v_{i} \rangle \thinspace \langle v_{i} \rvert\right)\right)\right)\right) \land  \\ \left(B = \left(\sum_{i=1}^{n} \left(b_{i} \cdot \left(\lvert v_{i} \rangle \thinspace \langle v_{i} \rvert\right)\right)\right)\right) \end{array}\right)\end{array} \textrm{ if } \left\{v_{1}, v_{2}, \ldots, v_{n}\right\} \in \textrm{O.N.Bases}\left(\mathbb{C}^{n}\right)\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	parameters: 14 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 67 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10
8	Lambda	parameters: 11 body: 12
9	Operation	operator: 13 operands: 14
10	Operation	operator: 15 operand: 22
11	ExprTuple	17, 18
12	Conditional	value: 19 condition: 20
13	Literal
14	ExprTuple	21
15	Literal
16	ExprTuple	22
17	ExprRange	lambda_map: 23 start_index: 81 end_index: 82
18	ExprRange	lambda_map: 24 start_index: 81 end_index: 82
19	Operation	operator: 26 operands: 25
20	Operation	operator: 26 operands: 27
21	ExprRange	lambda_map: 28 start_index: 81 end_index: 82
22	Operation	operator: 29 operands: 30
23	Lambda	parameter: 63 body: 54
24	Lambda	parameter: 63 body: 55
25	ExprTuple	31, 32
26	Literal
27	ExprTuple	33, 34
28	Lambda	parameter: 63 body: 35
29	Literal
30	ExprTuple	56, 82
31	Operation	operator: 37 operands: 36
32	Operation	operator: 37 operands: 38
33	ExprRange	lambda_map: 39 start_index: 81 end_index: 82
34	ExprRange	lambda_map: 40 start_index: 81 end_index: 82
35	IndexedVar	variable: 87 index: 63
36	ExprTuple	41, 42
37	Literal
38	ExprTuple	43, 44
39	Lambda	parameter: 63 body: 45
40	Lambda	parameter: 63 body: 46
41	Variable
42	Operation	operator: 48 operand: 52
43	Variable
44	Operation	operator: 48 operand: 53
45	Operation	operator: 67 operands: 50
46	Operation	operator: 67 operands: 51
47	ExprTuple	52
48	Literal
49	ExprTuple	53
50	ExprTuple	54, 56
51	ExprTuple	55, 56
52	Lambda	parameter: 89 body: 57
53	Lambda	parameter: 89 body: 58
54	IndexedVar	variable: 73 index: 63
55	IndexedVar	variable: 74 index: 63
56	Literal
57	Conditional	value: 60 condition: 62
58	Conditional	value: 61 condition: 62
59	ExprTuple	63
60	Operation	operator: 65 operands: 64
61	Operation	operator: 65 operands: 66
62	Operation	operator: 67 operands: 68
63	Variable
64	ExprTuple	69, 71
65	Literal
66	ExprTuple	70, 71
67	Literal
68	ExprTuple	89, 72
69	IndexedVar	variable: 73 index: 89
70	IndexedVar	variable: 74 index: 89
71	Operation	operator: 75 operands: 76
72	Operation	operator: 77 operands: 78
73	Variable
74	Variable
75	Literal
76	ExprTuple	79, 80
77	Literal
78	ExprTuple	81, 82
79	Operation	operator: 83 operand: 86
80	Operation	operator: 84 operand: 86
81	Literal
82	Variable
83	Literal
84	Literal
85	ExprTuple	86
86	IndexedVar	variable: 87 index: 89
87	Variable
88	ExprTuple	89
89	Variable