def deriveCommonConclusion(self, conclusion, assumptions=USE_DEFAULTS):
'''
From (A or B) derive and return the provided conclusion C assuming A=>C, B=>C, A,B,C in BOOLEANS.
'''
from ._theorems_ import hypotheticalDisjunction
from proveit.logic import Implies, compose
# forall_{A in Bool, B in Bool, C in Bool} (A=>C and B=>C) => ((A or B) => C)
assert len(self.operands) == 2
leftOperand, rightOperand = self.operands
leftImplConclusion = Implies(leftOperand, conclusion)
rightImplConclusion = Implies(rightOperand, conclusion)
# (A=>C and B=>C) assuming A=>C, B=>C
compose([leftImplConclusion, rightImplConclusion], assumptions)
return hypotheticalDisjunction.specialize(
{
A: leftOperand,
B: rightOperand,
C: conclusion
},
assumptions=assumptions).deriveConclusion(
assumptions).deriveConclusion(assumptions)
def derive_common_conclusion(self, conclusion, assumptions=USE_DEFAULTS):
'''
From (A or B) derive and return the provided conclusion C assuming A=>C, B=>C, A,B,C in BOOLEANS.
'''
from . import hypothetical_disjunction
from proveit.logic import Implies, compose
# forall_{A in Bool, B in Bool, C in Bool} (A=>C and B=>C) => ((A or B)
# => C)
assert self.operands.is_double()
left_operand, right_operand = self.operands
left_impl_conclusion = Implies(left_operand, conclusion)
right_impl_conclusion = Implies(right_operand, conclusion)
# (A=>C and B=>C) assuming A=>C, B=>C
compose([left_impl_conclusion, right_impl_conclusion], assumptions)
return hypothetical_disjunction.instantiate(
{
A: left_operand,
B: right_operand,
C: conclusion
},
assumptions=assumptions).derive_conclusion(
assumptions).derive_conclusion(assumptions)