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, 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 And, CartExp, 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([v_1_to_n, w_1_to_n], Conditional(InSet(VecSum(index_or_indices = [i], summand = Qmult(Ket(v_i), Bra(w_i)), domain = Interval(one, n)), Unitary(n)), And(InSet(Set(v_1_to_n_kets), sub_expr1), InSet(Set(w_1_to_n_kets), sub_expr1)))))

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}, w_{1}, w_{2}, \ldots, w_{n}\right) \mapsto \left\{\left(\sum_{i=1}^{n} \left(\lvert v_{i} \rangle \thinspace \langle w_{i} \rvert\right)\right) \in \textrm{U}\left(n\right) \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(\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)\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, 5
3	Conditional	value: 6 condition: 7
4	ExprRange	lambda_map: 8 start_index: 61 end_index: 62
5	ExprRange	lambda_map: 9 start_index: 61 end_index: 62
6	Operation	operator: 39 operands: 10
7	Operation	operator: 11 operands: 12
8	Lambda	parameter: 75 body: 70
9	Lambda	parameter: 75 body: 71
10	ExprTuple	13, 14
11	Literal
12	ExprTuple	15, 16
13	Operation	operator: 17 operand: 23
14	Operation	operator: 19 operand: 62
15	Operation	operator: 39 operands: 21
16	Operation	operator: 39 operands: 22
17	Literal
18	ExprTuple	23
19	Literal
20	ExprTuple	62
21	ExprTuple	24, 26
22	ExprTuple	25, 26
23	Lambda	parameter: 69 body: 27
24	Operation	operator: 42 operand: 34
25	Operation	operator: 42 operand: 35
26	Operation	operator: 30 operand: 36
27	Conditional	value: 32 condition: 33
28	ExprTuple	34
29	ExprTuple	35
30	Literal
31	ExprTuple	36
32	Operation	operator: 37 operands: 38
33	Operation	operator: 39 operands: 40
34	Operation	operator: 42 operands: 41
35	Operation	operator: 42 operands: 43
36	Operation	operator: 44 operands: 45
37	Literal
38	ExprTuple	46, 47
39	Literal
40	ExprTuple	69, 48
41	ExprTuple	49
42	Literal
43	ExprTuple	50
44	Literal
45	ExprTuple	51, 62
46	Operation	operator: 67 operand: 59
47	Operation	operator: 53 operand: 60
48	Operation	operator: 55 operands: 56
49	ExprRange	lambda_map: 57 start_index: 61 end_index: 62
50	ExprRange	lambda_map: 58 start_index: 61 end_index: 62
51	Literal
52	ExprTuple	59
53	Literal
54	ExprTuple	60
55	Literal
56	ExprTuple	61, 62
57	Lambda	parameter: 75 body: 63
58	Lambda	parameter: 75 body: 64
59	IndexedVar	variable: 72 index: 69
60	IndexedVar	variable: 73 index: 69
61	Literal
62	Variable
63	Operation	operator: 67 operand: 70
64	Operation	operator: 67 operand: 71
65	ExprTuple	69
66	ExprTuple	70
67	Literal
68	ExprTuple	71
69	Variable
70	IndexedVar	variable: 72 index: 75
71	IndexedVar	variable: 73 index: 75
72	Variable
73	Variable
74	ExprTuple	75
75	Variable