theorem
  L.v = 0.GF iff not v in Carrier(L)
proof
  thus L.v = 0.GF implies not v in Carrier(L)
  proof
    assume
A1: L.v = 0.GF;
    assume not thesis;
    then ex u st u = v & L.u <> 0.GF;
    hence thesis by A1;
  end;
  assume not v in Carrier(L);
  hence thesis;
end;
