 reserve RNS1,RNS2 for RealLinearSpace;

theorem Th5:
the RLSStruct of RNS1 = the RLSStruct of RNS2
implies
  for q be Element of RNS1,
      g be Element of RNS2
     st q = g
  holds -q = -g
proof
assume A1: the RLSStruct of RNS1 = the RLSStruct of RNS2;
let q be Element of RNS1,
    g be Element of RNS2;
assume A2: q = g;
thus -q = (-1)*q by RLVECT_1:16
  .= (-1)*g by A2,A1
  .= -g by RLVECT_1:16;
end;
