Expression of type Forall

from the theory of proveit.core_expr_types.tuples

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import a, i, j, k, l
from proveit.core_expr_types.tuples import neg_shift_equiv
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Integer, Natural, one, subtract

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a], instance_expr = Forall(instance_param_or_params = [i, j, k, l], instance_expr = neg_shift_equiv, conditions = [InSet(subtract(subtract(j, one), i), Natural), Equals(k, subtract(i, a)), Equals(l, subtract(j, a))]), domain = Integer)

expr:

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

Passed sanity check: expr matches stored_expr

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

\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]

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: 6 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 65 body: 3
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 25 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	65, 10
9	Lambda	parameters: 11 body: 12
10	Literal
11	ExprTuple	63, 61, 50, 51
12	Conditional	value: 13 condition: 14
13	Operation	operator: 28 operands: 15
14	Operation	operator: 16 operands: 17
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	20, 21, 22
18	ExprTuple	23
19	ExprTuple	24
20	Operation	operator: 25 operands: 26
21	Operation	operator: 28 operands: 27
22	Operation	operator: 28 operands: 29
23	ExprRange	lambda_map: 30 start_index: 53 end_index: 31
24	ExprRange	lambda_map: 32 start_index: 33 end_index: 34
25	Literal
26	ExprTuple	35, 36
27	ExprTuple	50, 37
28	Literal
29	ExprTuple	51, 38
30	Lambda	parameter: 70 body: 39
31	Operation	operator: 67 operand: 61
32	Lambda	parameter: 70 body: 41
33	Operation	operator: 67 operand: 50
34	Operation	operator: 67 operand: 51
35	Operation	operator: 59 operands: 44
36	Literal
37	Operation	operator: 59 operands: 45
38	Operation	operator: 59 operands: 46
39	Operation	operator: 48 operand: 64
40	ExprTuple	61
41	Operation	operator: 48 operand: 55
42	ExprTuple	50
43	ExprTuple	51
44	ExprTuple	52, 53
45	ExprTuple	63, 54
46	ExprTuple	61, 54
47	ExprTuple	64
48	Variable
49	ExprTuple	55
50	Variable
51	Variable
52	Operation	operator: 59 operands: 56
53	Operation	operator: 67 operand: 63
54	Operation	operator: 67 operand: 65
55	Operation	operator: 59 operands: 60
56	ExprTuple	61, 62
57	ExprTuple	63
58	ExprTuple	65
59	Literal
60	ExprTuple	64, 65
61	Variable
62	Operation	operator: 67 operand: 69
63	Variable
64	Operation	operator: 67 operand: 70
65	Variable
66	ExprTuple	69
67	Literal
68	ExprTuple	70
69	Literal
70	Variable