
theorem Th18:
  for x,y,z being set st x <> [<*y,z*>,and2] & y <> [<*z,x*>,and2]
  & z <> [<*x,y*>,and2] holds x in InputVertices GFA0CarryStr(x,y,z) & y in
  InputVertices GFA0CarryStr(x,y,z) & z in InputVertices GFA0CarryStr(x,y,z)
proof
  set f1 = and2, f2 = and2, f3 = and2;
  let x,y,z be set;
  assume x <> [<*y,z*>,f2] & y <> [<*z,x*>,f3] & z <> [<*x,y*>,f1];
  then InputVertices GFA0CarryStr(x,y,z) = {x,y,z} by Th14;
  hence thesis by ENUMSET1:def 1;
end;
