Theorem range_len_typical_eq of type Forall

from the theory of proveit.core_expr_types.tuples

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.core_expr_types.tuples import range_len_typical_eq

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

Passed sanity check: range_len_typical_eq matches stored_expr

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

\forall_{f, i, j~|~\left(j - i + 1\right) \in \mathbb{N}}~\left(|\left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right)\right)| = |\left(i, \left(i + 1\right), \ldots, j\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	32, 31, 27
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12, 13
10	Literal
11	ExprTuple	14, 15
12	Operation	operator: 17 operands: 16
13	Operation	operator: 17 operands: 18
14	Operation	operator: 19 operands: 20
15	Literal
16	ExprTuple	21
17	Literal
18	ExprTuple	22
19	Literal
20	ExprTuple	27, 23, 24
21	ExprRange	lambda_map: 25 start_index: 31 end_index: 27
22	ExprRange	lambda_map: 26 start_index: 31 end_index: 27
23	Operation	operator: 28 operand: 31
24	Literal
25	Lambda	parameter: 34 body: 30
26	Lambda	parameter: 34 body: 34
27	Variable
28	Literal
29	ExprTuple	31
30	Operation	operator: 32 operand: 34
31	Variable
32	Variable
33	ExprTuple	34
34	Variable