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 CartExp, Forall, InSet, Set
from proveit.numbers import Complex, Interval, NaturalPos, 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(n, Conditional(Forall(instance_param_or_params = [v_1_to_n, w_1_to_n], instance_expr = InSet(VecSum(index_or_indices = [i], summand = Qmult(Ket(v_i), Bra(w_i)), domain = Interval(one, n)), Unitary(n)), conditions = [InSet(Set(v_1_to_n_kets), sub_expr1), InSet(Set(w_1_to_n_kets), sub_expr1)]).with_wrapping(), InSet(n, NaturalPos))))

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