# 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.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import 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 = 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 \in \left(a,b\right)\right) = \left(\left(x \in \mathbb{R}\right) \land \left(a < x < b\right)\right)

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 12
operands: 5
4Operationoperator: 14
operands: 6
5ExprTuple23, 7
6ExprTuple8, 9
7Operationoperator: 10
operands: 11
8Operationoperator: 12
operands: 13
9Operationoperator: 14
operands: 15
10Literal
11ExprTuple22, 24
12Literal
13ExprTuple23, 16
14Literal
15ExprTuple17, 18
16Literal
17Operationoperator: 20
operands: 19
18Operationoperator: 20
operands: 21
19ExprTuple22, 23
20Literal
21ExprTuple23, 24
22Variable
23Variable
24Variable