Theorem ortho_norm_bases_form_unitary_matrix of type Forall

from the theory of proveit.physics.quantum.algebra

see dependencies

import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_theorem_expr # Load the stored theorem expression as 'stored_expr'
# import the special expression
from proveit.physics.quantum.algebra import ortho_norm_bases_form_unitary_matrix

# check that the built expression is the same as the stored expression
assert ortho_norm_bases_form_unitary_matrix.expr == stored_expr
assert ortho_norm_bases_form_unitary_matrix.expr._style_id == stored_expr._style_id
print("Passed sanity check: ortho_norm_bases_form_unitary_matrix matches stored_expr")

Passed sanity check: ortho_norm_bases_form_unitary_matrix matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{n \in \mathbb{N}^+}~\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}\right]

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 6 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 71 body: 3
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 48 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	71, 10
9	Lambda	parameters: 11 body: 12
10	Literal
11	ExprTuple	13, 14
12	Conditional	value: 15 condition: 16
13	ExprRange	lambda_map: 17 start_index: 70 end_index: 71
14	ExprRange	lambda_map: 18 start_index: 70 end_index: 71
15	Operation	operator: 48 operands: 19
16	Operation	operator: 20 operands: 21
17	Lambda	parameter: 84 body: 79
18	Lambda	parameter: 84 body: 80
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	24, 25
22	Operation	operator: 26 operand: 32
23	Operation	operator: 28 operand: 71
24	Operation	operator: 48 operands: 30
25	Operation	operator: 48 operands: 31
26	Literal
27	ExprTuple	32
28	Literal
29	ExprTuple	71
30	ExprTuple	33, 35
31	ExprTuple	34, 35
32	Lambda	parameter: 78 body: 36
33	Operation	operator: 51 operand: 43
34	Operation	operator: 51 operand: 44
35	Operation	operator: 39 operand: 45
36	Conditional	value: 41 condition: 42
37	ExprTuple	43
38	ExprTuple	44
39	Literal
40	ExprTuple	45
41	Operation	operator: 46 operands: 47
42	Operation	operator: 48 operands: 49
43	Operation	operator: 51 operands: 50
44	Operation	operator: 51 operands: 52
45	Operation	operator: 53 operands: 54
46	Literal
47	ExprTuple	55, 56
48	Literal
49	ExprTuple	78, 57
50	ExprTuple	58
51	Literal
52	ExprTuple	59
53	Literal
54	ExprTuple	60, 71
55	Operation	operator: 76 operand: 68
56	Operation	operator: 62 operand: 69
57	Operation	operator: 64 operands: 65
58	ExprRange	lambda_map: 66 start_index: 70 end_index: 71
59	ExprRange	lambda_map: 67 start_index: 70 end_index: 71
60	Literal
61	ExprTuple	68
62	Literal
63	ExprTuple	69
64	Literal
65	ExprTuple	70, 71
66	Lambda	parameter: 84 body: 72
67	Lambda	parameter: 84 body: 73
68	IndexedVar	variable: 81 index: 78
69	IndexedVar	variable: 82 index: 78
70	Literal
71	Variable
72	Operation	operator: 76 operand: 79
73	Operation	operator: 76 operand: 80
74	ExprTuple	78
75	ExprTuple	79
76	Literal
77	ExprTuple	80
78	Variable
79	IndexedVar	variable: 81 index: 84
80	IndexedVar	variable: 82 index: 84
81	Variable
82	Variable
83	ExprTuple	84
84	Variable