Theorem extended_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 extended_range_len_typical_eq

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

Passed sanity check: extended_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, x}~\left[\forall_{i, j~|~|\left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right)\right)| \in \mathbb{N}}~\left(|\left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right), x\right)| = |\left(i, \left(i + 1\right), \ldots, \left(j + 1\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	parameters: 3 body: 4
3	ExprTuple	36, 24
4	Operation	operator: 5 operand: 7
5	Literal
6	ExprTuple	7
7	Lambda	parameters: 8 body: 9
8	ExprTuple	30, 34
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
16	Operation	operator: 22 operands: 20
17	Operation	operator: 22 operands: 21
18	Operation	operator: 22 operands: 23
19	Literal
20	ExprTuple	26, 24
21	ExprTuple	25
22	Literal
23	ExprTuple	26
24	Variable
25	ExprRange	lambda_map: 27 start_index: 30 end_index: 28
26	ExprRange	lambda_map: 29 start_index: 30 end_index: 34
27	Lambda	parameter: 38 body: 38
28	Operation	operator: 31 operands: 32
29	Lambda	parameter: 38 body: 33
30	Variable
31	Literal
32	ExprTuple	34, 35
33	Operation	operator: 36 operand: 38
34	Variable
35	Literal
36	Variable
37	ExprTuple	38
38	Variable