Theorem not_int_if_not_int_in_interval of type Forall

from the theory of proveit.numbers.number_sets.real_numbers

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.numbers.number_sets.real_numbers import not_int_if_not_int_in_interval

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

Passed sanity check: not_int_if_not_int_in_interval matches stored_expr

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

\forall_{n \in \mathbb{Z}}~\left[\forall_{x \in \left(n - 1,n + 1\right)~|~x \neq n}~\left(x \notin \mathbb{Z}\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: 7 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 36 body: 4
3	ExprTuple	36
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 22 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	36, 19
10	Lambda	parameter: 27 body: 12
11	ExprTuple	27
12	Conditional	value: 13 condition: 14
13	Operation	operator: 15 operands: 16
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	27, 19
17	Literal
18	ExprTuple	20, 21
19	Literal
20	Operation	operator: 22 operands: 23
21	Operation	operator: 24 operands: 25
22	Literal
23	ExprTuple	27, 26
24	Literal
25	ExprTuple	27, 36
26	Operation	operator: 28 operands: 29
27	Variable
28	Literal
29	ExprTuple	30, 31
30	Operation	operator: 33 operands: 32
31	Operation	operator: 33 operands: 34
32	ExprTuple	36, 35
33	Literal
34	ExprTuple	36, 39
35	Operation	operator: 37 operand: 39
36	Variable
37	Literal
38	ExprTuple	39
39	Literal