
theorem Th81:
  for x,y,z being set st x <> [<*y,z*>,and2c] & y <> [<*z,x*>,
nor2] & z <> [<*x,y*>,and2a] holds x in InputVertices GFA2CarryStr(x,y,z) & y
  in InputVertices GFA2CarryStr(x,y,z) & z in InputVertices GFA2CarryStr(x,y,z)
proof
  set f1 = and2a, f2 = and2c, f3 = nor2;
  let x,y,z be set;
  assume x <> [<*y,z*>,f2] & y <> [<*z,x*>,f3] & z <> [<*x,y*>,f1];
  then InputVertices GFA2CarryStr(x,y,z) = {x,y,z} by Th77;
  hence thesis by ENUMSET1:def 1;
end;
