Theorem extended_range_from1_len 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_from1_len

# check that the built expression is the same as the stored expression
assert extended_range_from1_len.expr == stored_expr
assert extended_range_from1_len.expr._style_id == stored_expr._style_id
print("Passed sanity check: extended_range_from1_len matches stored_expr")

Passed sanity check: extended_range_from1_len matches stored_expr

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

\forall_{i \in \mathbb{N}}~\left[\forall_{f, x}~\left(|\left(f\left(1\right), f\left(2\right), \ldots, f\left(i\right), x\right)| = \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: 7 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 27 body: 4
3	ExprTuple	27
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 11
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11
9	Literal
10	ExprTuple	27, 12
11	Lambda	parameters: 13 body: 14
12	Literal
13	ExprTuple	29, 24
14	Operation	operator: 15 operands: 16
15	Literal
16	ExprTuple	17, 18
17	Operation	operator: 19 operands: 20
18	Operation	operator: 21 operands: 22
19	Literal
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	27, 26
23	ExprRange	lambda_map: 25 start_index: 26 end_index: 27
24	Variable
25	Lambda	parameter: 31 body: 28
26	Literal
27	Variable
28	Operation	operator: 29 operand: 31
29	Variable
30	ExprTuple	31
31	Variable