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.
# import Expression classes needed to build the expression
from proveit import Conditional, x
from proveit.logic import Equals
from proveit.numbers import Abs, LessEq, Neg, zero

In [2]:
# build up the expression from sub-expressions
expr = 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\{\left|x\right| = \left(-x\right) \textrm{ if } x \leq 0\right..

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 3
operands: 4
2Operationoperator: 5
operands: 6
3Literal
4ExprTuple7, 8
5Literal
6ExprTuple13, 9
7Operationoperator: 10
operand: 13
8Operationoperator: 11
operand: 13
9Literal
10Literal
11Literal
12ExprTuple13
13Variable