# from the theory of proveit.numbers.absolute_value¶

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.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, ExprTuple, Lambda, x
from proveit.logic import Equals
from proveit.numbers import Abs, LessEq, Neg, zero

In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda(x, Conditional(Equals(Abs(x), Neg(x)), LessEq(x, zero))))

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 \mapsto \left\{\left|x\right| = \left(-x\right) \textrm{ if } x \leq 0\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
1Lambdaparameter: 15
body: 2
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operands: 6
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9, 10
7Literal
8ExprTuple15, 11
9Operationoperator: 12
operand: 15
10Operationoperator: 13
operand: 15
11Literal
12Literal
13Literal
14ExprTuple15
15Variable