Theorem partition 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 partition

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

Passed sanity check: partition matches stored_expr

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

\forall_{f, i, j, k~|~\left(\left(j + 1\right) - i\right) \in \mathbb{N}, \left(k - j\right) \in \mathbb{N}}~\left(\begin{array}{c} \begin{array}{l} \left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(k\right)\right) =  \\ \left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right),f\left(j + 1\right), f\left(j + 2\right), \ldots, f\left(k\right)\right) \end{array} \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: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameters: 4 body: 5
4	ExprTuple	29, 42, 43, 33
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	ExprTuple	16
13	ExprTuple	17, 18
14	Operation	operator: 20 operands: 19
15	Operation	operator: 20 operands: 21
16	ExprRange	lambda_map: 22 start_index: 42 end_index: 33
17	ExprRange	lambda_map: 22 start_index: 42 end_index: 43
18	ExprRange	lambda_map: 22 start_index: 31 end_index: 33
19	ExprTuple	23, 25
20	Literal
21	ExprTuple	24, 25
22	Lambda	parameter: 35 body: 26
23	Operation	operator: 36 operands: 27
24	Operation	operator: 36 operands: 28
25	Literal
26	Operation	operator: 29 operand: 35
27	ExprTuple	31, 32
28	ExprTuple	33, 34
29	Variable
30	ExprTuple	35
31	Operation	operator: 36 operands: 37
32	Operation	operator: 39 operand: 42
33	Variable
34	Operation	operator: 39 operand: 43
35	Variable
36	Literal
37	ExprTuple	43, 41
38	ExprTuple	42
39	Literal
40	ExprTuple	43
41	Literal
42	Variable
43	Variable