def __init__(self, operator, lhs, rhs):
TransitiveRelation.__init__(self, operator, lhs, rhs)
# The lower bound side of this inequality.
# (regardless of the 'direction' style).
self.lower = self.operands[0]
# The upper bound side of this inequality.
self.upper = self.operands[1]
def apply_transitivity(self, other, assumptions=USE_DEFAULTS):
'''
apply_transitivity(Subset(A,B), SetEquiv(B,C))
returns Subset(A,C)
'''
from proveit.logic import Equals, SetEquiv, SubsetEq
if isinstance(other, Equals):
return TransitiveRelation.apply_transitivity(
self, other, assumptions)
if isinstance(other, SetEquiv):
# From set equivalence, derive the appropriate subset_eq
# so we can use normal subset transitivity.
if other.lhs == self.superset or other.rhs == self.subset:
# EITHER (A subset B) and (B set_equiv C)
# OR (A subset B) and (C set_equiv A)
other_as_subset_eq = SubsetEq(*other.operands.entries)
elif other.rhs == self.superset or other.lhs == self.subset:
# EITHER (A subset B) and (C set_equiv B)
# OR (A subset B) and (A set_equiv C)
other_as_subset_eq = SubsetEq(
*reversed(other.operands.entries))
else:
raise ValueError("Unable to apply transitivity between %s "
"and %s." % (self, other))
return self.apply_transitivity(other_as_subset_eq, assumptions)
def side_effects(self, judgment):
'''
In addition to the TransitiveRelation side-effects, also
attempt derive_relaxed (if applicable) and derive_reversed.
'''
for side_effect in TransitiveRelation.side_effects(self, judgment):
yield side_effect
if hasattr(self, 'derive_relaxed'):
yield self.derive_relaxed
def sideEffects(self, knownTruth):
'''
In addition to the TransitiveRelation side-effects, also
attempt deriveRelaxed (if applicable) and deriveReversed.
'''
for sideEffect in TransitiveRelation.sideEffects(self, knownTruth):
yield sideEffect
if hasattr(self, 'deriveRelaxed'):
yield self.deriveRelaxed
yield self.deriveReversed
def side_effects(self, judgment):
'''
In addition to the TransitiveRelation side-effects, also
attempt derive_negated, derive_relaxed (if applicable),
and derive_reversed.
'''
for side_effect in TransitiveRelation.side_effects(self, judgment):
yield side_effect
# yield self.derive_negated # Needs to be implemented (again)
if hasattr(self, 'derive_relaxed'):
yield self.derive_relaxed
def __init__(self, operator, lhs, rhs):
TransitiveRelation.__init__(self, operator, lhs, rhs)
def __init__(self, operator, lhs, rhs, *, styles):
TransitiveRelation.__init__(self, operator, lhs, rhs, styles=styles)
self.subset = self.operands[0]
self.superset = self.operands[1]