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 shift_equiv
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Add, 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 = shift_equiv, conditions = [InSet(subtract(Add(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: 60 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	60, 10
9	Lambda	parameters: 11 body: 12
10	Literal
11	ExprTuple	58, 56, 34, 36
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: 58 end_index: 56
24	ExprRange	lambda_map: 31 start_index: 34 end_index: 36
25	Literal
26	ExprTuple	32, 33
27	ExprTuple	34, 35
28	Literal
29	ExprTuple	36, 37
30	Lambda	parameter: 59 body: 38
31	Lambda	parameter: 59 body: 39
32	Operation	operator: 54 operands: 40
33	Literal
34	Variable
35	Operation	operator: 54 operands: 41
36	Variable
37	Operation	operator: 54 operands: 42
38	Operation	operator: 44 operand: 59
39	Operation	operator: 44 operand: 49
40	ExprTuple	46, 47
41	ExprTuple	58, 48
42	ExprTuple	56, 48
43	ExprTuple	59
44	Variable
45	ExprTuple	49
46	Operation	operator: 54 operands: 50
47	Operation	operator: 52 operand: 58
48	Operation	operator: 52 operand: 60
49	Operation	operator: 54 operands: 55
50	ExprTuple	56, 57
51	ExprTuple	58
52	Literal
53	ExprTuple	60
54	Literal
55	ExprTuple	59, 60
56	Variable
57	Literal
58	Variable
59	Variable
60	Variable