def build_T7(F, G):
# (F->G)->((!F->G)->G)
nF = notFormula(F)
nG = notFormula(G)
F1 = Node(F, G)
F1.msg = "t7 hypoth"
F2 = Node(nF, G)
F2.msg = "t7 hypoth"
f3 = build_T5(F, G)
F3 = f3[-1]
F4 = axiom.A3(F, G)
f5 = syl_1(F3, F4)
F5 = f5[-1]
F6 = MP(F1, F5)
f7 = build_T4(nG, F)
F7 = f7[-1]
# (!F->G)->(!F->!!G)
F8 = nF
F9 = Node(nF, G)
F10 = MP(F8, F9)
f11 = build_T2(G)
F11 = f11[-1]
F12 = MP(F10, F11)
f13 = build_deduction([F1, F2, F9], F8, F12, [F8, F9, F10] + f11 + [F12])
F13 = f13[-1]
f14 = build_deduction([], F9, F13, f13)
F14 = f14[-1]
#...
f15 = syl_1(F14, F7)
F15 = f15[-1]
f16 = syl_1(F15, F6)
F16 = f16[-1]
proof = [F1, F2] + f14 + [F4] + f5
f17 = build_deduction([], F1, F16, proof)
proof = f17
return proof
def build_T4(F, G):
# (!G->!F)->(F->G)
nF = notFormula(F)
nG = notFormula(G)
F1 = Node(nG, nF)
F2 = F
F3 = axiom.A3(F, G)
F4 = MP(F1, F3)
F5 = axiom.A1(F, nG)
f6 = syl_1(F5, F4)
proof = [F3, F4, F5]
proof.extend(f6)
proof = build_deduction([F1, F], F1, f6[-1], proof)
return proof
def build_T2(F):
nF = notFormula(F) # !F
nnF = notFormula(nF) # !!F
nnnF = notFormula(nnF) # !!!F
F1 = axiom.A3(F, nnF) # (!!!F->!F)->((!!F->F)->!!F)
f2 = build_T1(nF) # build th. 1
F2 = f2[-1] # !!!A->!A
F3 = MP(F2, F1) # ...->!!A
F4 = axiom.A1(F, nnnF) # A->...
f5 = syl_1(F4, F3) # f5[-1] = A->!!A
res = [F1]
res.extend(f2)
res.extend([F3, F4])
res.extend(f5)
return res
def build_T5(F, G):
"""
(F->G)->(!G->!F)
"""
nF = notFormula(F)
nG = notFormula(G)
nnF = notFormula(nF)
nnG = notFormula(nG)
F1 = Node(F, G)
f2 = build_T2(G)
F2 = f2[-1]
F3 = axiom.A3(nG, nF)
f4 = syl_1(F1, F2) # f->!!g
F4 = f4[-1]
f5 = build_T1(F)
F5 = f5[-1]
f6 = syl_1(F5, F4) # !!f->!!g
F6 = f6[-1]
F7 = MP(F6, F3) # (!!f->!g)->!f
F8 = axiom.A1(nG, nnF)
f9 = syl_1(F8, F7)
F9 = f9[-1]
proof = f2 + [F3] + f4 + f5 + f6 + [F7, F8] + f9
proof = build_deduction([F1, nG], F1, F9, proof)
return proof
def build_T3(F, G):
# !f -> (f->G)
nG = notFormula(G)
F1 = notFormula(F)
F2 = F
F3 = axiom.A1(F2, nG)
F4 = MP(F2, F3)
F5 = axiom.A1(F1, nG)
F6 = MP(F1, F5)
F7 = axiom.A3(F, G)
F8 = MP(F6, F7)
F9 = MP(F4, F8)
proof = [F1, F2, F3, F4, F5, F6, F7, F8, F9]
ded1 = build_deduction([F1], F, G, proof)
proof = ded1
ded2 = build_deduction([], F1, ded1[-1], proof)
proof = ded2
return proof
def build_T1(F):
nF = notFormula(F)
F1 = axiom.A3(nF, F)
f2 = build_TL(nF)
F2 = f2[-1]
f3 = syl_2(F1, F2)
F3 = f3[-1]
nnF = notFormula(nF)
F4 = axiom.A1(nnF, nF)
f5 = syl_1(F4, F3)
F5 = f5[-1]
res = [F1]
res.extend(f2)
res.extend(f3)
res.extend([F4])
res.extend(f5)
return res