Theorem range_2_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_2_expansion

# check that the built expression is the same as the stored expression
assert range_2_expansion.expr == stored_expr
assert range_2_expansion.expr._style_id == stored_expr._style_id
print("Passed sanity check: range_2_expansion matches stored_expr")

Passed sanity check: range_2_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 + 1\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)\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	22, 27, 17
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	17, 21
11	ExprTuple	13
12	ExprTuple	14, 15
13	ExprRange	lambda_map: 16 start_index: 27 end_index: 17
14	Operation	operator: 22 operand: 27
15	Operation	operator: 22 operand: 21
16	Lambda	parameter: 26 body: 20
17	Variable
18	ExprTuple	27
19	ExprTuple	21
20	Operation	operator: 22 operand: 26
21	Operation	operator: 24 operands: 25
22	Variable
23	ExprTuple	26
24	Literal
25	ExprTuple	27, 28
26	Variable
27	Variable
28	Literal