Theorem completeness_relation 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 completeness_relation

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

Passed sanity check: completeness_relation matches stored_expr

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

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