Theorem range_9_expansion of type Forall

from the theory of proveit.numbers.numerals.decimals

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.numerals.decimals import range_9_expansion

# check that the built expression is the same as the stored expression
assert range_9_expansion.expr == stored_expr
assert range_9_expansion.expr._style_id == stored_expr._style_id
print("Passed sanity check: range_9_expansion matches stored_expr")

Passed sanity check: range_9_expansion matches stored_expr

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

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