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, n
from proveit.logic import And, InSet
from proveit.numbers import Integer, Interval, LessEq

# build up the expression from sub-expressions
expr = Conditional(InSet(n, Interval(a, b)), And(InSet(a, Integer), InSet(b, Integer), InSet(n, Integer), And(LessEq(a, n), LessEq(n, b)).with_total_ordering_style()))

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\{n \in \{a~\ldotp \ldotp~b\} \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  n \in \mathbb{Z} ,  a \leq n \leq b\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: 14 operands: 3
2	Operation	operator: 16 operands: 4
3	ExprTuple	25, 5
4	ExprTuple	6, 7, 8, 9
5	Operation	operator: 10 operands: 11
6	Operation	operator: 14 operands: 12
7	Operation	operator: 14 operands: 13
8	Operation	operator: 14 operands: 15
9	Operation	operator: 16 operands: 17
10	Literal
11	ExprTuple	24, 26
12	ExprTuple	24, 18
13	ExprTuple	26, 18
14	Literal
15	ExprTuple	25, 18
16	Literal
17	ExprTuple	19, 20
18	Literal
19	Operation	operator: 22 operands: 21
20	Operation	operator: 22 operands: 23
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	25, 26
24	Variable
25	Variable
26	Variable