# from the theory of proveit.numbers.number_sets.integers¶

In [1]:
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.
# 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

In [2]:
# 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:
In [3]:
# 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

In [4]:
# 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..

In [5]:
stored_expr.style_options()

no style options
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Lambdaparameters: 1
body: 2
1ExprTuple26, 28, 27
2Conditionalvalue: 3
condition: 4
3Operationoperator: 16
operands: 5
4Operationoperator: 18
operands: 6
5ExprTuple27, 7
6ExprTuple8, 9, 10, 11
7Operationoperator: 12
operands: 13
8Operationoperator: 16
operands: 14
9Operationoperator: 16
operands: 15
10Operationoperator: 16
operands: 17
11Operationoperator: 18
operands: 19
12Literal
13ExprTuple26, 28
14ExprTuple26, 20
15ExprTuple28, 20
16Literal
17ExprTuple27, 20
18Literal
19ExprTuple21, 22
20Literal
21Operationoperator: 24
operands: 23
22Operationoperator: 24
operands: 25
23ExprTuple26, 27
24Literal
25ExprTuple27, 28
26Variable
27Variable
28Variable