Theorem redundant_mod_elimination_in_sum of type Forall

from the theory of proveit.numbers.modular

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.modular import redundant_mod_elimination_in_sum

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

Passed sanity check: redundant_mod_elimination_in_sum matches stored_expr

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

\forall_{i, j \in \mathbb{N}}~\left[\forall_{a_{1}, a_{2}, \ldots, a_{i}, b, c_{1}, c_{2}, \ldots, c_{j} \in \mathbb{R}}~\left[\forall_{L \in \mathbb{R}^+}~\left(\begin{array}{c} \begin{array}{l} \left(\left(a_{1} +  a_{2} +  \ldots +  a_{i} + \left(b ~\textup{mod}~ L\right)+ c_{1} +  c_{2} +  \ldots +  c_{j}\right) ~\textup{mod}~ L\right) =  \\ \left(\left(a_{1} +  a_{2} +  \ldots +  a_{i} + b+ c_{1} +  c_{2} +  \ldots +  c_{j}\right) ~\textup{mod}~ L\right) \end{array} \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: 18 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 3 body: 4
3	ExprTuple	58, 61
4	Conditional	value: 5 condition: 6
5	Operation	operator: 18 operand: 9
6	Operation	operator: 20 operands: 8
7	ExprTuple	9
8	ExprTuple	10, 11
9	Lambda	parameters: 51 body: 12
10	Operation	operator: 39 operands: 13
11	Operation	operator: 39 operands: 14
12	Conditional	value: 15 condition: 16
13	ExprTuple	58, 17
14	ExprTuple	61, 17
15	Operation	operator: 18 operand: 22
16	Operation	operator: 20 operands: 21
17	Literal
18	Literal
19	ExprTuple	22
20	Literal
21	ExprTuple	23, 24, 25
22	Lambda	parameter: 63 body: 27
23	ExprRange	lambda_map: 28 start_index: 60 end_index: 58
24	Operation	operator: 39 operands: 29
25	ExprRange	lambda_map: 30 start_index: 60 end_index: 61
26	ExprTuple	63
27	Conditional	value: 31 condition: 32
28	Lambda	parameter: 69 body: 33
29	ExprTuple	62, 44
30	Lambda	parameter: 69 body: 34
31	Operation	operator: 35 operands: 36
32	Operation	operator: 39 operands: 37
33	Operation	operator: 39 operands: 38
34	Operation	operator: 39 operands: 40
35	Literal
36	ExprTuple	41, 42
37	ExprTuple	63, 43
38	ExprTuple	64, 44
39	Literal
40	ExprTuple	65, 44
41	Operation	operator: 55 operands: 45
42	Operation	operator: 55 operands: 46
43	Literal
44	Literal
45	ExprTuple	47, 63
46	ExprTuple	48, 63
47	Operation	operator: 50 operands: 49
48	Operation	operator: 50 operands: 51
49	ExprTuple	53, 52, 54
50	Literal
51	ExprTuple	53, 62, 54
52	Operation	operator: 55 operands: 56
53	ExprRange	lambda_map: 57 start_index: 60 end_index: 58
54	ExprRange	lambda_map: 59 start_index: 60 end_index: 61
55	Literal
56	ExprTuple	62, 63
57	Lambda	parameter: 69 body: 64
58	Variable
59	Lambda	parameter: 69 body: 65
60	Literal
61	Variable
62	Variable
63	Variable
64	IndexedVar	variable: 66 index: 69
65	IndexedVar	variable: 67 index: 69
66	Variable
67	Variable
68	ExprTuple	69
69	Variable