Theorem general_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 general_len

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

Passed sanity check: general_len matches stored_expr

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

\forall_{n \in \mathbb{N}^+}~\left[\begin{array}{l}\forall_{f_{1}, f_{2}, \ldots, f_{n}, i_{1}, i_{2}, \ldots, i_{n}, j_{1}, j_{2}, \ldots, j_{n}~|~\left(\left(j_{1} - i_{1} + 1\right) \in \mathbb{N}\right), \left(\left(j_{2} - i_{2} + 1\right) \in \mathbb{N}\right), \ldots, \left(\left(j_{n} - i_{n} + 1\right) \in \mathbb{N}\right)}~\\
\left(\begin{array}{c} \begin{array}{l} |\left(f_{1}\left(i_{1}\right), f_{1}\left(i_{1} + 1\right), \ldots, f_{1}\left(j_{1}\right), f_{2}\left(i_{2}\right), f_{2}\left(i_{2} + 1\right), \ldots, f_{2}\left(j_{2}\right), \ldots\ldots, f_{n}\left(i_{n}\right), f_{n}\left(i_{n} + 1\right), \ldots, f_{n}\left(j_{n}\right)\right)| \\  = \left(\left(j_{1} - i_{1} + 1\right) +  \left(j_{2} - i_{2} + 1\right) +  \ldots +  \left(j_{n} - i_{n} + 1\right)\right) \end{array} \end{array}\right)\end{array}\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: 39 body: 4
3	ExprTuple	39
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 40 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	39, 11
10	Lambda	parameters: 12 body: 13
11	Literal
12	ExprTuple	14, 15, 16
13	Conditional	value: 17 condition: 18
14	ExprRange	lambda_map: 19 start_index: 53 end_index: 39
15	ExprRange	lambda_map: 20 start_index: 53 end_index: 39
16	ExprRange	lambda_map: 21 start_index: 53 end_index: 39
17	Operation	operator: 22 operands: 23
18	Operation	operator: 24 operands: 25
19	Lambda	parameter: 64 body: 26
20	Lambda	parameter: 64 body: 60
21	Lambda	parameter: 64 body: 51
22	Literal
23	ExprTuple	27, 28
24	Literal
25	ExprTuple	29
26	IndexedVar	variable: 58 index: 64
27	Operation	operator: 30 operands: 31
28	Operation	operator: 48 operands: 32
29	ExprRange	lambda_map: 33 start_index: 53 end_index: 39
30	Literal
31	ExprTuple	34
32	ExprTuple	35
33	Lambda	parameter: 64 body: 36
34	ExprRange	lambda_map: 37 start_index: 53 end_index: 39
35	ExprRange	lambda_map: 38 start_index: 53 end_index: 39
36	Operation	operator: 40 operands: 41
37	Lambda	parameter: 61 body: 42
38	Lambda	parameter: 64 body: 43
39	Variable
40	Literal
41	ExprTuple	43, 44
42	ExprRange	lambda_map: 45 start_index: 46 end_index: 47
43	Operation	operator: 48 operands: 49
44	Literal
45	Lambda	parameter: 64 body: 50
46	IndexedVar	variable: 62 index: 61
47	IndexedVar	variable: 55 index: 61
48	Literal
49	ExprTuple	51, 52, 53
50	Operation	operator: 54 operand: 64
51	IndexedVar	variable: 55 index: 64
52	Operation	operator: 56 operand: 60
53	Literal
54	IndexedVar	variable: 58 index: 61
55	Variable
56	Literal
57	ExprTuple	60
58	Variable
59	ExprTuple	61
60	IndexedVar	variable: 62 index: 64
61	Variable
62	Variable
63	ExprTuple	64
64	Variable