Theorem sum_split_after 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_after

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

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