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, M, i, n
from proveit.core_expr_types import a_1_to_n, a_i, v_1_to_n, v_i
from proveit.linear_algebra import Hspace, OrthoNormBases, ScalarMult, VecSum
from proveit.logic import Equals, Exists, InSet, Set
from proveit.numbers import Complex, Interval, one
from proveit.physics.quantum import Bra, Ket, Qmult
from proveit.physics.quantum.algebra import v_1_to_n_kets

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([v_1_to_n], Conditional(Exists(instance_param_or_params = [a_1_to_n], instance_expr = Equals(M, VecSum(index_or_indices = [i], summand = ScalarMult(a_i, Qmult(Ket(v_i), Bra(v_i))), domain = Interval(one, n))), domain = Complex).with_wrapping(), InSet(Set(v_1_to_n_kets), OrthoNormBases(Hspace)))))

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