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, ExprTuple, 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 Commutator, Hspace, LinMap, OrthoNormBases, ScalarMult, VecSum, VecZero
from proveit.logic import And, 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(Equals(Commutator(A, B), VecZero(LinMap(Hspace, Hspace))), Exists(instance_param_or_params = [v_1_to_n], instance_expr = 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(), condition = InSet(Set(v_1_to_n), OrthoNormBases(Hspace))).with_wrapping())

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[A, B\right] = \vec{0}\left(\mathcal{L}\left(\mathcal{H}, \mathcal{H}\right)\right), \begin{array}{l}\exists_{v_{1}, v_{2}, \ldots, v_{n}~|~\left\{v_{1}, v_{2}, \ldots, v_{n}\right\} \in \textrm{O.N.Bases}\left(\mathcal{H}\right)}~\\
\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}\right]\end{array}\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
1	Operation	operator: 48 operands: 3
2	Operation	operator: 18 operand: 7
3	ExprTuple	5, 6
4	ExprTuple	7
5	Operation	operator: 8 operands: 9
6	Operation	operator: 10 operand: 13
7	Lambda	parameters: 27 body: 12
8	Literal
9	ExprTuple	52, 54
10	Literal
11	ExprTuple	13
12	Conditional	value: 14 condition: 15
13	Operation	operator: 16 operands: 17
14	Operation	operator: 18 operand: 21
15	Operation	operator: 78 operands: 20
16	Literal
17	ExprTuple	35, 35
18	Literal
19	ExprTuple	21
20	ExprTuple	22, 23
21	Lambda	parameters: 24 body: 25
22	Operation	operator: 26 operands: 27
23	Operation	operator: 28 operand: 35
24	ExprTuple	30, 31
25	Conditional	value: 32 condition: 33
26	Literal
27	ExprTuple	34
28	Literal
29	ExprTuple	35
30	ExprRange	lambda_map: 36 start_index: 92 end_index: 93
31	ExprRange	lambda_map: 37 start_index: 92 end_index: 93
32	Operation	operator: 39 operands: 38
33	Operation	operator: 39 operands: 40
34	ExprRange	lambda_map: 41 start_index: 92 end_index: 93
35	Variable
36	Lambda	parameter: 74 body: 65
37	Lambda	parameter: 74 body: 66
38	ExprTuple	42, 43
39	Literal
40	ExprTuple	44, 45
41	Lambda	parameter: 74 body: 46
42	Operation	operator: 48 operands: 47
43	Operation	operator: 48 operands: 49
44	ExprRange	lambda_map: 50 start_index: 92 end_index: 93
45	ExprRange	lambda_map: 51 start_index: 92 end_index: 93
46	IndexedVar	variable: 98 index: 74
47	ExprTuple	52, 53
48	Literal
49	ExprTuple	54, 55
50	Lambda	parameter: 74 body: 56
51	Lambda	parameter: 74 body: 57
52	Variable
53	Operation	operator: 59 operand: 63
54	Variable
55	Operation	operator: 59 operand: 64
56	Operation	operator: 78 operands: 61
57	Operation	operator: 78 operands: 62
58	ExprTuple	63
59	Literal
60	ExprTuple	64
61	ExprTuple	65, 67
62	ExprTuple	66, 67
63	Lambda	parameter: 100 body: 68
64	Lambda	parameter: 100 body: 69
65	IndexedVar	variable: 84 index: 74
66	IndexedVar	variable: 85 index: 74
67	Literal
68	Conditional	value: 71 condition: 73
69	Conditional	value: 72 condition: 73
70	ExprTuple	74
71	Operation	operator: 76 operands: 75
72	Operation	operator: 76 operands: 77
73	Operation	operator: 78 operands: 79
74	Variable
75	ExprTuple	80, 82
76	Literal
77	ExprTuple	81, 82
78	Literal
79	ExprTuple	100, 83
80	IndexedVar	variable: 84 index: 100
81	IndexedVar	variable: 85 index: 100
82	Operation	operator: 86 operands: 87
83	Operation	operator: 88 operands: 89
84	Variable
85	Variable
86	Literal
87	ExprTuple	90, 91
88	Literal
89	ExprTuple	92, 93
90	Operation	operator: 94 operand: 97
91	Operation	operator: 95 operand: 97
92	Literal
93	Variable
94	Literal
95	Literal
96	ExprTuple	97
97	IndexedVar	variable: 98 index: 100
98	Variable
99	ExprTuple	100
100	Variable