# from the theory of proveit.numbers.negation¶

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
from proveit.logic import Equals, InSet
from proveit.numbers import Complex, Neg

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

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(-\left(-x\right)\right) = x \textrm{ if } x \in \mathbb{C}\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, 15
7Literal
8ExprTuple15, 10
9Operationoperator: 13
operand: 12
10Literal
11ExprTuple12
12Operationoperator: 13
operand: 15
13Literal
14ExprTuple15
15Variable