Theorem factorization_from_scalars of type Forall

from the theory of proveit.linear_algebra.scalar_multiplication

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.scalar_multiplication import factorization_from_scalars

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

Passed sanity check: factorization_from_scalars matches stored_expr

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

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