# 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, Lambda, x, y, z
from proveit.logic import And
from proveit.numbers import LessEq

In [2]:
# build up the expression from sub-expressions
expr = 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(x, y, z\right) \mapsto \left\{x \leq z \textrm{ if } x \leq y ,  y \leq z\right..

In [5]:
stored_expr.style_options()

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

core typesub-expressionsexpression
0Lambdaparameters: 1
body: 2
1ExprTuple13, 14, 15
2Conditionalvalue: 3
condition: 4
3Operationoperator: 11
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple13, 15
6Literal
7ExprTuple8, 9
8Operationoperator: 11
operands: 10
9Operationoperator: 11
operands: 12
10ExprTuple13, 14
11Literal
12ExprTuple14, 15
13Variable
14Variable
15Variable