Theorem subtraction_disassociation of type Forall

from the theory of proveit.numbers.addition.subtraction

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.numbers.addition.subtraction import subtraction_disassociation

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

Passed sanity check: subtraction_disassociation matches stored_expr

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

\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 \mathbb{C}}~\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]

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: 7 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 3 body: 4
3	ExprTuple	45, 67, 48
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 24 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	11, 12, 13
10	Lambda	parameters: 14 body: 15
11	Operation	operator: 51 operands: 16
12	Operation	operator: 51 operands: 17
13	Operation	operator: 51 operands: 18
14	ExprTuple	37, 64, 39
15	Conditional	value: 19 condition: 20
16	ExprTuple	45, 21
17	ExprTuple	67, 21
18	ExprTuple	48, 21
19	Operation	operator: 22 operands: 23
20	Operation	operator: 24 operands: 25
21	Literal
22	Literal
23	ExprTuple	26, 27
24	Literal
25	ExprTuple	28, 29, 30
26	Operation	operator: 58 operands: 31
27	Operation	operator: 58 operands: 32
28	ExprRange	lambda_map: 33 start_index: 66 end_index: 45
29	ExprRange	lambda_map: 34 start_index: 66 end_index: 67
30	ExprRange	lambda_map: 35 start_index: 66 end_index: 48
31	ExprTuple	37, 36, 39
32	ExprTuple	37, 38, 39
33	Lambda	parameter: 71 body: 40
34	Lambda	parameter: 71 body: 41
35	Lambda	parameter: 71 body: 42
36	Operation	operator: 60 operand: 53
37	ExprRange	lambda_map: 44 start_index: 66 end_index: 45
38	ExprRange	lambda_map: 46 start_index: 66 end_index: 67
39	ExprRange	lambda_map: 47 start_index: 66 end_index: 48
40	Operation	operator: 51 operands: 49
41	Operation	operator: 51 operands: 50
42	Operation	operator: 51 operands: 52
43	ExprTuple	53
44	Lambda	parameter: 71 body: 55
45	Variable
46	Lambda	parameter: 71 body: 54
47	Lambda	parameter: 71 body: 56
48	Variable
49	ExprTuple	55, 57
50	ExprTuple	68, 57
51	Literal
52	ExprTuple	56, 57
53	Operation	operator: 58 operands: 59
54	Operation	operator: 60 operand: 68
55	IndexedVar	variable: 62 index: 71
56	IndexedVar	variable: 63 index: 71
57	Literal
58	Literal
59	ExprTuple	64
60	Literal
61	ExprTuple	68
62	Variable
63	Variable
64	ExprRange	lambda_map: 65 start_index: 66 end_index: 67
65	Lambda	parameter: 71 body: 68
66	Literal
67	Variable
68	IndexedVar	variable: 69 index: 71
69	Variable
70	ExprTuple	71
71	Variable