# 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, Lambda, x
from proveit.logic import Equals, InSet
from proveit.numbers import Complex, Mult, Neg, one

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

x \mapsto \left\{\left(\left(-1\right) \cdot x\right) = \left(-x\right) \textrm{ if } x \in \mathbb{C}\right..

In [5]:
stored_expr.style_options()

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

core typesub-expressionsexpression
0Lambdaparameter: 15
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 4
operands: 5
3Operationoperator: 6
operands: 7
4Literal
5ExprTuple8, 9
6Literal
7ExprTuple15, 10
8Operationoperator: 11
operands: 12
9Operationoperator: 16
operand: 15
10Literal
11Literal
12ExprTuple14, 15
13ExprTuple15
14Operationoperator: 16
operand: 18
15Variable
16Literal
17ExprTuple18
18Literal