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, Forall, InSet
from proveit.numbers import Integer, Interval, LessEq

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

\left\{\forall_{n \in \{a~\ldotp \ldotp~b\}}~\left(a \leq n \leq b\right) \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z}\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 operand: 6
2	Operation	operator: 16 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameter: 28 body: 10
7	Operation	operator: 18 operands: 11
8	Operation	operator: 18 operands: 12
9	ExprTuple	28
10	Conditional	value: 13 condition: 14
11	ExprTuple	29, 15
12	ExprTuple	30, 15
13	Operation	operator: 16 operands: 17
14	Operation	operator: 18 operands: 19
15	Literal
16	Literal
17	ExprTuple	20, 21
18	Literal
19	ExprTuple	28, 22
20	Operation	operator: 24 operands: 23
21	Operation	operator: 24 operands: 25
22	Operation	operator: 26 operands: 27
23	ExprTuple	29, 28
24	Literal
25	ExprTuple	28, 30
26	Literal
27	ExprTuple	29, 30
28	Variable
29	Variable
30	Variable