Theorem disassociation 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 disassociation

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

Passed sanity check: disassociation 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, j, k \in \mathbb{N}}~\left[\forall_{a_{1}, a_{2}, \ldots, a_{i}, b_{1}, b_{2}, \ldots, b_{j}, c_{1}, c_{2}, \ldots, c_{k} \in V}~\left(\begin{array}{c} \begin{array}{l} \left(a_{1} +  a_{2} +  \ldots +  a_{i} + \left(b_{1} +  b_{2} +  \ldots +  b_{j}\right)+ c_{1} +  c_{2} +  \ldots +  c_{k}\right) =  \\ \left(a_{1} +  a_{2} +  \ldots +  a_{i}+ b_{1} +  b_{2} +  \ldots +  b_{j}+ c_{1} +  c_{2} +  \ldots +  c_{k}\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: 69 body: 7
6	ExprTuple	69
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	69, 14
13	Lambda	parameters: 15 body: 16
14	Operation	operator: 17 operand: 21
15	ExprTuple	59, 72, 61
16	Conditional	value: 19 condition: 20
17	Literal
18	ExprTuple	21
19	Operation	operator: 22 operand: 25
20	Operation	operator: 38 operands: 24
21	Variable
22	Literal
23	ExprTuple	25
24	ExprTuple	26, 27, 28
25	Lambda	parameters: 46 body: 29
26	Operation	operator: 64 operands: 30
27	Operation	operator: 64 operands: 31
28	Operation	operator: 64 operands: 32
29	Conditional	value: 33 condition: 34
30	ExprTuple	59, 35
31	ExprTuple	72, 35
32	ExprTuple	61, 35
33	Operation	operator: 36 operands: 37
34	Operation	operator: 38 operands: 39
35	Literal
36	Literal
37	ExprTuple	40, 41
38	Literal
39	ExprTuple	42, 43, 44
40	Operation	operator: 56 operands: 45
41	Operation	operator: 56 operands: 46
42	ExprRange	lambda_map: 47 start_index: 71 end_index: 59
43	ExprRange	lambda_map: 48 start_index: 71 end_index: 72
44	ExprRange	lambda_map: 49 start_index: 71 end_index: 61
45	ExprTuple	51, 50, 52
46	ExprTuple	51, 66, 52
47	Lambda	parameter: 78 body: 53
48	Lambda	parameter: 78 body: 54
49	Lambda	parameter: 78 body: 55
50	Operation	operator: 56 operands: 57
51	ExprRange	lambda_map: 58 start_index: 71 end_index: 59
52	ExprRange	lambda_map: 60 start_index: 71 end_index: 61
53	Operation	operator: 64 operands: 62
54	Operation	operator: 64 operands: 63
55	Operation	operator: 64 operands: 65
56	Literal
57	ExprTuple	66
58	Lambda	parameter: 78 body: 67
59	Variable
60	Lambda	parameter: 78 body: 68
61	Variable
62	ExprTuple	67, 69
63	ExprTuple	75, 69
64	Literal
65	ExprTuple	68, 69
66	ExprRange	lambda_map: 70 start_index: 71 end_index: 72
67	IndexedVar	variable: 73 index: 78
68	IndexedVar	variable: 74 index: 78
69	Variable
70	Lambda	parameter: 78 body: 75
71	Literal
72	Variable
73	Variable
74	Variable
75	IndexedVar	variable: 76 index: 78
76	Variable
77	ExprTuple	78
78	Variable