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, U, i, n
from proveit.core_expr_types import v_1_to_n, v_i, w_1_to_n, w_i
from proveit.linear_algebra import OrthoNormBases, Unitary, VecSum
from proveit.logic import CartExp, 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, w_1_to_n_kets

# build up the expression from sub-expressions
sub_expr1 = OrthoNormBases(CartExp(Complex, n))
expr = ExprTuple(Lambda(U, Conditional(Exists(instance_param_or_params = [v_1_to_n, w_1_to_n], instance_expr = Equals(U, VecSum(index_or_indices = [i], summand = Qmult(Ket(v_i), Bra(w_i)), domain = Interval(one, n))), conditions = [InSet(Set(v_1_to_n_kets), sub_expr1), InSet(Set(w_1_to_n_kets), sub_expr1)]).with_wrapping(), InSet(U, Unitary(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(U \mapsto \left\{\begin{array}{l}\exists_{v_{1}, v_{2}, \ldots, v_{n}, w_{1}, w_{2}, \ldots, w_{n}~|~\left\{\left\{\lvert v_{1} \rangle, \lvert v_{2} \rangle, \ldots, \lvert v_{n} \rangle\right\}\right\} \in \textrm{O.N.Bases}\left(\mathbb{C}^{n}\right), \left\{\left\{\lvert w_{1} \rangle, \lvert w_{2} \rangle, \ldots, \lvert w_{n} \rangle\right\}\right\} \in \textrm{O.N.Bases}\left(\mathbb{C}^{n}\right)}~\\
\left(U = \left(\sum_{i=1}^{n} \left(\lvert v_{i} \rangle \thinspace \langle w_{i} \rvert\right)\right)\right)\end{array} \textrm{ if } U \in \textrm{U}\left(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	parameter: 25 body: 3
2	ExprTuple	25
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 49 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	25, 10
9	Lambda	parameters: 11 body: 12
10	Operation	operator: 13 operand: 72
11	ExprTuple	15, 16
12	Conditional	value: 17 condition: 18
13	Literal
14	ExprTuple	72
15	ExprRange	lambda_map: 19 start_index: 71 end_index: 72
16	ExprRange	lambda_map: 20 start_index: 71 end_index: 72
17	Operation	operator: 21 operands: 22
18	Operation	operator: 23 operands: 24
19	Lambda	parameter: 85 body: 80
20	Lambda	parameter: 85 body: 81
21	Literal
22	ExprTuple	25, 26
23	Literal
24	ExprTuple	27, 28
25	Variable
26	Operation	operator: 29 operand: 33
27	Operation	operator: 49 operands: 31
28	Operation	operator: 49 operands: 32
29	Literal
30	ExprTuple	33
31	ExprTuple	34, 36
32	ExprTuple	35, 36
33	Lambda	parameter: 79 body: 37
34	Operation	operator: 52 operand: 44
35	Operation	operator: 52 operand: 45
36	Operation	operator: 40 operand: 46
37	Conditional	value: 42 condition: 43
38	ExprTuple	44
39	ExprTuple	45
40	Literal
41	ExprTuple	46
42	Operation	operator: 47 operands: 48
43	Operation	operator: 49 operands: 50
44	Operation	operator: 52 operands: 51
45	Operation	operator: 52 operands: 53
46	Operation	operator: 54 operands: 55
47	Literal
48	ExprTuple	56, 57
49	Literal
50	ExprTuple	79, 58
51	ExprTuple	59
52	Literal
53	ExprTuple	60
54	Literal
55	ExprTuple	61, 72
56	Operation	operator: 77 operand: 69
57	Operation	operator: 63 operand: 70
58	Operation	operator: 65 operands: 66
59	ExprRange	lambda_map: 67 start_index: 71 end_index: 72
60	ExprRange	lambda_map: 68 start_index: 71 end_index: 72
61	Literal
62	ExprTuple	69
63	Literal
64	ExprTuple	70
65	Literal
66	ExprTuple	71, 72
67	Lambda	parameter: 85 body: 73
68	Lambda	parameter: 85 body: 74
69	IndexedVar	variable: 82 index: 79
70	IndexedVar	variable: 83 index: 79
71	Literal
72	Variable
73	Operation	operator: 77 operand: 80
74	Operation	operator: 77 operand: 81
75	ExprTuple	79
76	ExprTuple	80
77	Literal
78	ExprTuple	81
79	Variable
80	IndexedVar	variable: 82 index: 85
81	IndexedVar	variable: 83 index: 85
82	Variable
83	Variable
84	ExprTuple	85
85	Variable