Theorem distribution_over_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 distribution_over_scalars

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

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