# 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 ExprTuple, 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 = ExprTuple(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())

\left(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)\right)

In [5]:
stored_expr.style_options()

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

core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameter: 26
body: 3
2ExprTuple26
3Operationoperator: 4
operands: 5
4Literal
5ExprTuple6, 7
6Operationoperator: 15
operands: 8
7Operationoperator: 17
operands: 9
8ExprTuple26, 10
9ExprTuple11, 12
10Operationoperator: 13
operands: 14
11Operationoperator: 15
operands: 16
12Operationoperator: 17
operands: 18
13Literal
14ExprTuple25, 27
15Literal
16ExprTuple26, 19
17Literal
18ExprTuple20, 21
19Literal
20Operationoperator: 23
operands: 22
21Operationoperator: 23
operands: 24
22ExprTuple25, 26
23Literal
24ExprTuple26, 27
25Variable
26Variable
27Variable