# from the theory of proveit.numbers.ordering¶

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, x, y
from proveit.logic import And, Equals, InSet
from proveit.numbers import LessEq, Real

In [2]:
# build up the expression from sub-expressions
expr = Conditional(LessEq(x, y), And(InSet(x, Real), InSet(y, Real), Equals(x, y)))

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 \leq y \textrm{ if } x \in \mathbb{R} ,  y \in \mathbb{R} ,  x = y\right..

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 3
operands: 13
2Operationoperator: 4
operands: 5
3Literal
4Literal
5ExprTuple6, 7, 8
6Operationoperator: 10
operands: 9
7Operationoperator: 10
operands: 11
8Operationoperator: 12
operands: 13
9ExprTuple15, 14
10Literal
11ExprTuple16, 14
12Literal
13ExprTuple15, 16
14Literal
15Variable
16Variable