def substitute_falsehood(self, lambda_map, **defaults_config):
'''
Given not(A), derive P(A) from P(FALSE).
'''
from proveit.logic.equality import substitute_falsehood
from proveit.logic import Equals
from proveit.common import P
Plambda = Equals._lambda_expr(lambda_map, self.operand)
return substitute_falsehood.instantiate({x: self.operand, P: Plambda})
def substitute_falsehood(self, lambda_map, assumptions=USE_DEFAULTS):
'''
Given not(A), derive P(A) from P(False).
'''
from proveit.logic.equality import substitute_falsehood
from proveit.logic import Equals
from proveit.common import P
Plambda = Equals._lambda_expr(lambda_map, self.operand)
return substitute_falsehood.instantiate(
{x: self.operand, P: Plambda}, assumptions=assumptions)
def sub_right_side_into(self, lambda_map, assumptions=USE_DEFAULTS):
'''
From A equiv B, and given P(A), derive P(B) assuming P(A).
UNDER CONSTRUCTION, adapted from Equals class.
P(x) is provided via lambda_map as a Lambda expression or an
object that returns a Lambda expression when calling lambda_map()
(see proveit.lambda_map, proveit.lambda_map.SubExprRepl in
particular), or, if neither of those, an expression upon
which to perform a global replacement of self.lhs.
'''
from . import sub_right_side_into
from proveit.logic import Equals
Plambda = Equals._lambda_expr(lambda_map, self.lhs)
return sub_right_side_into.instantiate(
{
A: self.lhs,
B: self.rhs,
P: Plambda
}, assumptions=assumptions)
