Expression of type Lambda

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

# build up the expression from sub-expressions
expr = Lambda([a, b, n], 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(a, b, n\right) \mapsto \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()

no style options

# display the expression information
stored_expr.expr_info()

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