def conclude(self, assumptions):
from proveit.logic import InSet, NotEquals
from proveit.numbers import (Rational, RationalNonZero, RationalPos,
RationalNeg, RationalNonNeg, Less,
greater, greater_eq, zero)
# If we known the element is in Q, we may be able to
# prove that is in RationalNonZero, RationalPos, RationalNeg, or
# RationalNonNeg if we know its relation to zero.
if (self.number_set != Rational
and InSet(self.element, Rational).proven(assumptions)):
if self.number_set == RationalNonZero:
if NotEquals(self.element, zero).proven(assumptions):
from . import non_zero_rational_is_rational_non_zero
return non_zero_rational_is_rational_non_zero.instantiate(
{q: self.element}, assumptions=assumptions)
if self.number_set == RationalPos:
if greater(self.element, zero).proven(assumptions):
from . import positive_rational_is_rational_pos
return positive_rational_is_rational_pos.instantiate(
{q: self.element}, assumptions=assumptions)
if self.number_set == RationalNeg:
if Less(self.element, zero).proven():
from . import negative_rational_is_rational_neg
return negative_rational_is_rational_neg.instantiate(
{q: self.element}, assumptions=assumptions)
if self.number_set == RationalNonNeg:
if greater_eq(self.element, zero).proven():
from . import non_neg_rational_in_rational_neg
return non_neg_rational_in_rational_neg.instantiate(
{q: self.element}, assumptions=assumptions)
# Resort to the default NumberMembership.conclude strategies.
return NumberMembership.conclude(self, assumptions)
def conclude(self, **defaults_config):
from proveit.logic import NotEquals, InSet
from proveit.numbers import zero
if (InSet(self.element, Complex).proven()
and NotEquals(self.element, zero).proven()):
return self.conclude_as_last_resort()
return NumberMembership.conclude(self)
def conclude(self, **defaults_config):
from proveit import ProofFailure
from . import n_in_digits
# if we know the element is 0-9, then we can show it is a digit
try:
return NumberMembership.conclude(self)
except ProofFailure:
return n_in_digits.instantiate({n: self.element})
def conclude(self, assumptions=USE_DEFAULTS):
from proveit import ProofFailure
from . import n_in_digits
# if we know the element is 0-9, then we can show it is a digit
try:
return NumberMembership.conclude(self, assumptions=assumptions)
except ProofFailure:
return n_in_digits.instantiate({n: self.element},
assumptions=assumptions)
def conclude(self, **defaults_config):
if (InSet(self.element, Integer).proven()
and NotEquals(self.element, zero).proven()):
return self.conclude_as_last_resort()
return NumberMembership.conclude(self)
def __init__(self, element):
NumberMembership.__init__(self, element, IntegerNonZero)
def __init__(self, element, number_set):
NumberMembership.__init__(self, element, number_set)
def __init__(self, element):
NumberMembership.__init__(self, element, RealNonZero)
def conclude(self, **defaults_config):
from proveit.numbers import zero, LessEq
if (InSet(self.element, Real).proven() and
LessEq(self.element, zero).proven()):
return self.conclude_as_last_resort()
return NumberMembership.conclude(self)
def __init__(self, element):
NumberMembership.__init__(self, element, RealPos)
def __init__(self, element, domain):
NumberMembership.__init__(self, element, domain)
self.domain = domain
def conclude(self, **defaults_config):
from proveit.numbers import Rational, zero
if (InSet(self.element, Rational).proven() and
NotEquals(self.element, zero).proven()):
return self.conclude_as_last_resort()
return NumberMembership.conclude(self)
def __init__(self, element):
NumberMembership.__init__(self, element, ComplexNonZero)