Theorem range_8_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_8_expansion

# check that the built expression is the same as the stored expression
assert range_8_expansion.expr == stored_expr
assert range_8_expansion.expr._style_id == stored_expr._style_id
print("Passed sanity check: range_8_expansion matches stored_expr")

Passed sanity check: range_8_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 + 7\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)\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	40, 57, 23
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	23, 39
11	ExprTuple	13
12	ExprTuple	14, 15, 16, 17, 18, 19, 20, 21
13	ExprRange	lambda_map: 22 start_index: 57 end_index: 23
14	Operation	operator: 40 operand: 57
15	Operation	operator: 40 operand: 33
16	Operation	operator: 40 operand: 34
17	Operation	operator: 40 operand: 35
18	Operation	operator: 40 operand: 36
19	Operation	operator: 40 operand: 37
20	Operation	operator: 40 operand: 38
21	Operation	operator: 40 operand: 39
22	Lambda	parameter: 50 body: 32
23	Variable
24	ExprTuple	57
25	ExprTuple	33
26	ExprTuple	34
27	ExprTuple	35
28	ExprTuple	36
29	ExprTuple	37
30	ExprTuple	38
31	ExprTuple	39
32	Operation	operator: 40 operand: 50
33	Operation	operator: 48 operands: 42
34	Operation	operator: 48 operands: 43
35	Operation	operator: 48 operands: 44
36	Operation	operator: 48 operands: 45
37	Operation	operator: 48 operands: 46
38	Operation	operator: 48 operands: 47
39	Operation	operator: 48 operands: 49
40	Variable
41	ExprTuple	50
42	ExprTuple	57, 51
43	ExprTuple	57, 52
44	ExprTuple	57, 53
45	ExprTuple	57, 54
46	ExprTuple	57, 55
47	ExprTuple	57, 56
48	Literal
49	ExprTuple	57, 58
50	Variable
51	Literal
52	Literal
53	Literal
54	Literal
55	Literal
56	Literal
57	Variable
58	Literal