# 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, a
from proveit.logic import InSet
from proveit.numbers import IntegerNeg, NaturalPos, Neg
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda(a, Conditional(InSet(Neg(a), IntegerNeg), InSet(a, NaturalPos))))
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(a \mapsto \left\{\left(-a\right) \in \mathbb{Z}^{-} \textrm{ if } a \in \mathbb{N}^+\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: 13
body: 2
2Conditionalvalue: 3
condition: 4
3Operationoperator: 6
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple8, 9
6Literal
7ExprTuple13, 10
8Operationoperator: 11
operand: 13
9Literal
10Literal
11Literal
12ExprTuple13
13Variable