# 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, z
from proveit.logic import And
from proveit.numbers import LessEq

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

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, z\right) \mapsto \left\{x \leq z \textrm{ if } x \leq y ,  y \leq z\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: 2
body: 3
2ExprTuple14, 15, 16
3Conditionalvalue: 4
condition: 5
4Operationoperator: 12
operands: 6
5Operationoperator: 7
operands: 8
6ExprTuple14, 16
7Literal
8ExprTuple9, 10
9Operationoperator: 12
operands: 11
10Operationoperator: 12
operands: 13
11ExprTuple14, 15
12Literal
13ExprTuple15, 16
14Variable
15Variable
16Variable