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

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 Lambda, a, b, x
from proveit.logic import And, Equals, InSet
from proveit.numbers import IntervalOO, Less, Real

In [2]:
# build up the expression from sub-expressions
expr = Lambda(x, Equals(InSet(x, IntervalOO(a, b)), And(InSet(x, Real), And(Less(a, x), Less(x, 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())

x \mapsto \left(\left(x \in \left(a,b\right)\right) = \left(\left(x \in \mathbb{R}\right) \land \left(a < x < b\right)\right)\right)

In [5]:
stored_expr.style_options()

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

core typesub-expressionsexpression
0Lambdaparameter: 25
body: 2
1ExprTuple25
2Operationoperator: 3
operands: 4
3Literal
4ExprTuple5, 6
5Operationoperator: 14
operands: 7
6Operationoperator: 16
operands: 8
7ExprTuple25, 9
8ExprTuple10, 11
9Operationoperator: 12
operands: 13
10Operationoperator: 14
operands: 15
11Operationoperator: 16
operands: 17
12Literal
13ExprTuple24, 26
14Literal
15ExprTuple25, 18
16Literal
17ExprTuple19, 20
18Literal
19Operationoperator: 22
operands: 21
20Operationoperator: 22
operands: 23
21ExprTuple24, 25
22Literal
23ExprTuple25, 26
24Variable
25Variable
26Variable