Theorem shift_equivalence 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

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

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