Theorem shift_equivalence_both 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 shift_equivalence_both

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

Passed sanity check: shift_equivalence_both matches stored_expr

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

\forall_{f}~\left[\forall_{a, b \in \mathbb{Z}}~\left[\forall_{i, j, k, l~|~\left(\left(j + 1\right) - i\right) \in \mathbb{N}, \left(i + a\right) = \left(k + b\right), \left(j + a\right) = \left(l + b\right)}~\left(\left(f\left(i + a\right), f\left(\left(i + 1\right) + a\right), \ldots, f\left(j + a\right)\right) = \left(f\left(k + b\right), f\left(\left(k + 1\right) + b\right), \ldots, f\left(l + b\right)\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: 11 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 56 body: 4
3	ExprTuple	56
4	Operation	operator: 11 operand: 6
5	ExprTuple	6
6	Lambda	parameters: 7 body: 8
7	ExprTuple	73, 75
8	Conditional	value: 9 condition: 10
9	Operation	operator: 11 operand: 14
10	Operation	operator: 25 operands: 13
11	Literal
12	ExprTuple	14
13	ExprTuple	15, 16
14	Lambda	parameters: 17 body: 18
15	Operation	operator: 34 operands: 19
16	Operation	operator: 34 operands: 20
17	ExprTuple	72, 70, 60, 61
18	Conditional	value: 21 condition: 22
19	ExprTuple	73, 23
20	ExprTuple	75, 23
21	Operation	operator: 37 operands: 24
22	Operation	operator: 25 operands: 26
23	Literal
24	ExprTuple	27, 28
25	Literal
26	ExprTuple	29, 30, 31
27	ExprTuple	32
28	ExprTuple	33
29	Operation	operator: 34 operands: 35
30	Operation	operator: 37 operands: 36
31	Operation	operator: 37 operands: 38
32	ExprRange	lambda_map: 39 start_index: 72 end_index: 70
33	ExprRange	lambda_map: 40 start_index: 60 end_index: 61
34	Literal
35	ExprTuple	41, 42
36	ExprTuple	43, 44
37	Literal
38	ExprTuple	45, 46
39	Lambda	parameter: 74 body: 47
40	Lambda	parameter: 74 body: 49
41	Operation	operator: 68 operands: 50
42	Literal
43	Operation	operator: 68 operands: 51
44	Operation	operator: 68 operands: 52
45	Operation	operator: 68 operands: 53
46	Operation	operator: 68 operands: 54
47	Operation	operator: 56 operand: 62
48	ExprTuple	74
49	Operation	operator: 56 operand: 63
50	ExprTuple	58, 59
51	ExprTuple	72, 73
52	ExprTuple	60, 75
53	ExprTuple	70, 73
54	ExprTuple	61, 75
55	ExprTuple	62
56	Variable
57	ExprTuple	63
58	Operation	operator: 68 operands: 64
59	Operation	operator: 65 operand: 72
60	Variable
61	Variable
62	Operation	operator: 68 operands: 67
63	Operation	operator: 68 operands: 69
64	ExprTuple	70, 71
65	Literal
66	ExprTuple	72
67	ExprTuple	74, 73
68	Literal
69	ExprTuple	74, 75
70	Variable
71	Literal
72	Variable
73	Variable
74	Variable
75	Variable