# 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 Less, LessEq

In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda([x, y, z], Conditional(Less(x, z), And(Less(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 < z \textrm{ if } x < 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
2ExprTuple15, 16, 17
3Conditionalvalue: 4
condition: 5
4Operationoperator: 11
operands: 6
5Operationoperator: 7
operands: 8
6ExprTuple15, 17
7Literal
8ExprTuple9, 10
9Operationoperator: 11
operands: 12
10Operationoperator: 13
operands: 14
11Literal
12ExprTuple15, 16
13Literal
14ExprTuple16, 17
15Variable
16Variable
17Variable