Theorem sum_split_general of type Forall

from the theory of proveit.numbers.summation

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.summation import sum_split_general

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

Passed sanity check: sum_split_general matches stored_expr

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

\forall_{f}~\left[\forall_{a, b, c \in \mathbb{Z}~|~a \leq b \leq c}~\left(\left(\sum_{x = a}^{c} f\left(x\right)\right) = \left(\left(\sum_{x = a}^{b} f\left(x\right)\right) + \left(\sum_{x = b + 1}^{c} f\left(x\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: 5 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 52 body: 4
3	ExprTuple	52
4	Operation	operator: 5 operand: 7
5	Literal
6	ExprTuple	7
7	Lambda	parameters: 8 body: 9
8	ExprTuple	62, 67, 64
9	Conditional	value: 10 condition: 11
10	Operation	operator: 12 operands: 13
11	Operation	operator: 26 operands: 14
12	Literal
13	ExprTuple	15, 16
14	ExprTuple	17, 18, 19, 20
15	Operation	operator: 36 operand: 28
16	Operation	operator: 65 operands: 22
17	Operation	operator: 54 operands: 23
18	Operation	operator: 54 operands: 24
19	Operation	operator: 54 operands: 25
20	Operation	operator: 26 operands: 27
21	ExprTuple	28
22	ExprTuple	29, 30
23	ExprTuple	62, 31
24	ExprTuple	67, 31
25	ExprTuple	64, 31
26	Literal
27	ExprTuple	32, 33
28	Lambda	parameter: 57 body: 34
29	Operation	operator: 36 operand: 41
30	Operation	operator: 36 operand: 42
31	Literal
32	Operation	operator: 38 operands: 59
33	Operation	operator: 38 operands: 39
34	Conditional	value: 48 condition: 40
35	ExprTuple	41
36	Literal
37	ExprTuple	42
38	Literal
39	ExprTuple	67, 64
40	Operation	operator: 54 operands: 43
41	Lambda	parameter: 57 body: 44
42	Lambda	parameter: 57 body: 45
43	ExprTuple	57, 46
44	Conditional	value: 48 condition: 47
45	Conditional	value: 48 condition: 49
46	Operation	operator: 60 operands: 50
47	Operation	operator: 54 operands: 51
48	Operation	operator: 52 operand: 57
49	Operation	operator: 54 operands: 55
50	ExprTuple	62, 64
51	ExprTuple	57, 56
52	Variable
53	ExprTuple	57
54	Literal
55	ExprTuple	57, 58
56	Operation	operator: 60 operands: 59
57	Variable
58	Operation	operator: 60 operands: 61
59	ExprTuple	62, 67
60	Literal
61	ExprTuple	63, 64
62	Variable
63	Operation	operator: 65 operands: 66
64	Variable
65	Literal
66	ExprTuple	67, 68
67	Variable
68	Literal