Theorem norm_of_tensor_prod of type Forall

from the theory of proveit.linear_algebra.tensors

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.linear_algebra.tensors import norm_of_tensor_prod

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

Passed sanity check: norm_of_tensor_prod matches stored_expr

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

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