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, b, i, j, k, l
from proveit.core_expr_types.tuples import neg_shift_equiv_both
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Add, Natural, one, subtract

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

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_{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)

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