Theorem multi_vec_add_def of type Forall

from the theory of proveit.linear_algebra.addition

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.addition import multi_vec_add_def

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

Passed sanity check: multi_vec_add_def 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[\begin{array}{l}\forall_{x_{1}, x_{2}, \ldots, x_{n}, y \in V}~\\
\left(\left(x_{1} +  x_{2} +  \ldots +  x_{n} + y\right) = \left(\left(x_{1} +  x_{2} +  \ldots +  x_{n}\right) + y\right)\right)\end{array}\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: 50 body: 7
6	ExprTuple	50
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	50, 14
13	Lambda	parameter: 53 body: 16
14	Operation	operator: 17 operand: 21
15	ExprTuple	53
16	Conditional	value: 19 condition: 20
17	Literal
18	ExprTuple	21
19	Operation	operator: 22 operand: 25
20	Operation	operator: 47 operands: 24
21	Variable
22	Literal
23	ExprTuple	25
24	ExprTuple	53, 26
25	Lambda	parameters: 38 body: 27
26	Literal
27	Conditional	value: 28 condition: 29
28	Operation	operator: 30 operands: 31
29	Operation	operator: 32 operands: 33
30	Literal
31	ExprTuple	34, 35
32	Literal
33	ExprTuple	36, 37
34	Operation	operator: 45 operands: 38
35	Operation	operator: 45 operands: 39
36	ExprRange	lambda_map: 40 start_index: 52 end_index: 53
37	Operation	operator: 47 operands: 41
38	ExprTuple	49, 44
39	ExprTuple	42, 44
40	Lambda	parameter: 57 body: 43
41	ExprTuple	44, 50
42	Operation	operator: 45 operands: 46
43	Operation	operator: 47 operands: 48
44	Variable
45	Literal
46	ExprTuple	49
47	Literal
48	ExprTuple	54, 50
49	ExprRange	lambda_map: 51 start_index: 52 end_index: 53
50	Variable
51	Lambda	parameter: 57 body: 54
52	Literal
53	Variable
54	IndexedVar	variable: 55 index: 57
55	Variable
56	ExprTuple	57
57	Variable