def side_effects(self, judgment):
'''
In addition to the TransitiveRelation side-effects, also
attempt derive_reversed.
'''
for side_effect in TransitiveRelation.side_effects(self, judgment):
yield side_effect
yield self.derive_reversed
def side_effects(self, judgment):
'''
Yield the TransitiveRelation side-effects (which also records known_left_sides
and known_right_sides). Also derive the left and right implications,
derive the reversed version and attempt to derive equality.
'''
for side_effect in TransitiveRelation.side_effects(self, judgment):
yield side_effect
yield self.derive_left_implication # B=>A given A<=>B
yield self.derive_right_implication # A=>B given A<=>B
yield self.derive_reversed # B<=>A given A<=>B
# A=B given A<=>B (assuming A and B are in booleans)
yield self.derive_equality
def side_effects(self, judgment):
'''
In addition to the TransitiveRelation side-effects, also
attempt (where applicable) eliminate_dividen_exponent,
eliminate_common_exponent, and eliminate_common_factor.
'''
from proveit.numbers import two, Exp, Mult
for side_effect in TransitiveRelation.side_effects(self, judgment):
yield side_effect
# For each of the following, use the default assumptions to
# verify some conditions before yielding the side effect method
# (i.e. check using .proven() without arguments)
# for 2|(b^n), derive 2|b.
# (can be generalized to any prime number).
if self.lhs == two and isinstance(self.rhs, Exp):
try:
deduce_number_set(self.rhs.base)
deduce_number_set(self.rhs.exponent)
except UnsatisfiedPrerequisites:
pass
if (InSet(self.rhs.base, Integer).proven()
and InSet(self.rhs.exponent, Integer).proven()):
yield self.eliminate_dividend_exponent
# for (a^n)|(b^n)
if (isinstance(self.rhs, Exp) and isinstance(self.lhs, Exp)
and self.lhs.exponent == self.rhs.exponent):
try:
deduce_number_set(self.lhs.base)
deduce_number_set(self.rhs.base)
deduce_number_set(self.lhs.exponent)
except UnsatisfiedPrerequisites:
pass
if (InSet(self.lhs.base, Integer).proven()
and InSet(self.rhs.base, Integer).proven()
and InSet(self.lhs.exponent, NaturalPos).proven()):
yield self.eliminate_common_exponent
# for (ka)|(kb)
if (isinstance(self.lhs, Mult) and isinstance(self.rhs, Mult)):
operands_intersection = (set(self.lhs.operands).intersection(
set(self.lhs.operands)))
if (len(operands_intersection) > 0):
yield self.eliminate_common_factors
def side_effects(self, judgment):
'''
Yield the TransitiveRelation side-effects (which also records
known_left_sides nd known_right_sides). Also derive the consequent
as a side-effect if the antecedent is known to be true
(under the "side-effect" assumptions).
As a special case, if the consequent is FALSE, do
derive_via_contradiction.
'''
from proveit.logic.booleans import FALSE
for side_effect in TransitiveRelation.side_effects(self, judgment):
yield side_effect
if self.antecedent.proven():
yield self.derive_consequent # B given A=>B and A
if self.consequent == FALSE:
# Not(A) given A=>FALSE or A given Not(A)=>FALSE
yield self.derive_via_contradiction