def DM2():
a = Var("a")
b = Var("b")
prem = premise(Not(And(a, b))) #The original premise, ~(A && B)
d1 = premise(
Not(Or(Not(a), Not(b)))
) #d1 is the phrase required to run DL1 and DL2. I ran it as a premise, but it is assumed, NOT a premise
return doubleNeg(
notI(
arrowI(assume(Not(Or(Not(a), Not(b)))),
notE(andI(DL1(d1), DL2(d1), And(a, b)), prem, false()),
Arrow(Not(Or(Not(a), Not(b))), false())),
Not(Not(Or(Not(a), Not(b))))), Or(Not(a), Not(b)))
def DL2(p1):
a = Var("a")
b = Var("b")
return doubleNeg(
notI(
arrowI(
assume(Not(b)),
notE(orIR(assumed(Not(b)), Or(Not(a), Not(b))), p1, false()),
Arrow(Not(b), false())), Not(Not(b))), b)
def disSyl():
A = Var("a")
B = Var("b")
p1 = premise(Or(A, B))
p2 = premise(Not(B))
return orE(
p1, arrowI(assume(A), assumed(A), Arrow(A, A)),
arrowI(assume(B), FE(notE(assumed(B), p2, false()), A), Arrow(B, A)),
A)
def or_expr(tokens):
follow = [TType.TEOF, TType.TRPAREN, TType.TARROW]
lhs = and_expr(tokens)
while tokens[0].ttype == TType.TOR:
tokens.pop(0)
rhs = and_expr(tokens)
lhs = Or(lhs, rhs)
if tokens[0].ttype not in follow:
raise ParseException(tokens[0].pos, follow, tokens[0].val)
return lhs
def main():
try:
clear()
orComm().print_proof()
clear()
disSyl().print_proof()
clear()
DM1().print_proof()
clear()
a = Var("a")
b = Var("b")
dlPrem = premise(Not(Or(Not(a), Not(b))))
DL1(dlPrem).print_proof()
clear()
dlPrem = premise(Not(Or(Not(a), Not(b))))
DL2(dlPrem).print_proof()
clear()
DM2().print_proof()
except (ProofException) as e:
e.print()
def doubleNeg(p, a):
l1 = LEM(Or(a, Not(a)))
l2 = assume(a)
l3 = assumed(a)
l4 = arrowI(l2, l3, Arrow(a, a))
l5 = assume(Not(a))
l6 = assumed(Not(a))
l7 = notE(l6, p, false())
l8 = FE(l7, a)
l9 = arrowI(l5, l8, Arrow(Not(a), a))
l10 = orE(l1, l4, l9, a)
return l10
def orComm():
A = Var("a")
B = Var("b")
p1 = premise(Or(A, B))
return orE(
p1, arrowI(assume(A), orIR(assumed(A), Or(B, A)), Arrow(A, Or(B, A))),
arrowI(assume(B), orIL(assumed(B), Or(B, A)), Arrow(B, Or(B, A))),
Or(B, A))
def DM1():
A = Var("a")
B = Var("b")
p1 = premise(Or(Not(A), Not(B)))
end = Not(And(A, B))
A_B = And(A, B)
#I condensed parts of the proofs so I could substitute in things that made sense to me, otherwise I was going nuts
return orE(
p1,
arrowI(
assume(Not(A)),
notI(
arrowI(assume(A_B),
notE(andEL(assumed(A_B), A), assumed(Not(A)), false()),
Arrow(A_B, false())), Not(A_B)),
Arrow(Not(A), Not(A_B))),
arrowI(
assume(Not(B)),
notI(
arrowI(assume(A_B),
notE(andER(assumed(A_B), B), assumed(Not(B)), false()),
Arrow(A_B, false())), Not(A_B)),
Arrow(Not(B), Not(A_B))), end)