Expression of type Conditional

from the theory of proveit.numbers.number_sets.integers

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 Conditional, a, b, x
from proveit.logic import And, InSet, NotInSet, Or
from proveit.numbers import Integer, Interval, Less

# build up the expression from sub-expressions
expr = Conditional(NotInSet(x, Interval(a, b)), And(InSet(a, Integer), InSet(b, Integer), InSet(x, Integer), Or(Less(x, a), Less(b, x))))

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())

\left\{x \notin \{a~\ldotp \ldotp~b\} \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  x \in \mathbb{Z} ,  \left(x < a\right) \lor \left(b < x\right)\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	28, 7
5	Literal
6	ExprTuple	8, 9, 10, 11
7	Operation	operator: 12 operands: 13
8	Operation	operator: 16 operands: 14
9	Operation	operator: 16 operands: 15
10	Operation	operator: 16 operands: 17
11	Operation	operator: 18 operands: 19
12	Literal
13	ExprTuple	26, 27
14	ExprTuple	26, 20
15	ExprTuple	27, 20
16	Literal
17	ExprTuple	28, 20
18	Literal
19	ExprTuple	21, 22
20	Literal
21	Operation	operator: 24 operands: 23
22	Operation	operator: 24 operands: 25
23	ExprTuple	28, 26
24	Literal
25	ExprTuple	27, 28
26	Variable
27	Variable
28	Variable