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, f, 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 = [f], instance_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_{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: 52 body: 4
3	ExprTuple	52
4	Operation	operator: 10 operand: 6
5	ExprTuple	6
6	Lambda	parameter: 69 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	69, 14
13	Lambda	parameters: 15 body: 16
14	Literal
15	ExprTuple	67, 65, 54, 55
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: 57 end_index: 35
28	ExprRange	lambda_map: 36 start_index: 37 end_index: 38
29	Literal
30	ExprTuple	39, 40
31	ExprTuple	54, 41
32	Literal
33	ExprTuple	55, 42
34	Lambda	parameter: 74 body: 43
35	Operation	operator: 71 operand: 65
36	Lambda	parameter: 74 body: 45
37	Operation	operator: 71 operand: 54
38	Operation	operator: 71 operand: 55
39	Operation	operator: 63 operands: 48
40	Literal
41	Operation	operator: 63 operands: 49
42	Operation	operator: 63 operands: 50
43	Operation	operator: 52 operand: 68
44	ExprTuple	65
45	Operation	operator: 52 operand: 59
46	ExprTuple	54
47	ExprTuple	55
48	ExprTuple	56, 57
49	ExprTuple	67, 58
50	ExprTuple	65, 58
51	ExprTuple	68
52	Variable
53	ExprTuple	59
54	Variable
55	Variable
56	Operation	operator: 63 operands: 60
57	Operation	operator: 71 operand: 67
58	Operation	operator: 71 operand: 69
59	Operation	operator: 63 operands: 64
60	ExprTuple	65, 66
61	ExprTuple	67
62	ExprTuple	69
63	Literal
64	ExprTuple	68, 69
65	Variable
66	Operation	operator: 71 operand: 73
67	Variable
68	Operation	operator: 71 operand: 74
69	Variable
70	ExprTuple	73
71	Literal
72	ExprTuple	74
73	Literal
74	Variable