theorem Th54:
  u in v1 + W & u in v2 + W implies v1 + W = v2 + W
proof
  assume that
A1: u in v1 + W and
A2: u in v2 + W;
  thus v1 + W = u + W by A1,Th53
    .= v2 + W by A2,Th53;
end;
