# 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, ExprTuple, Lambda, 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 = ExprTuple(Lambda([x, y], 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(\left(x, y\right) \mapsto \left\{x \leq y \textrm{ if } x \in \mathbb{R} ,  y \in \mathbb{R} ,  x = y\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
1Lambdaparameters: 15
body: 2
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operands: 15
4Operationoperator: 6
operands: 7
5Literal
6Literal
7ExprTuple8, 9, 10
8Operationoperator: 12
operands: 11
9Operationoperator: 12
operands: 13
10Operationoperator: 14
operands: 15
11ExprTuple17, 16
12Literal
13ExprTuple18, 16
14Literal
15ExprTuple17, 18
16Literal
17Variable
18Variable