reserve a,b for Complex;
reserve V,X,Y for ComplexLinearSpace;
reserve u,u1,u2,v,v1,v2 for VECTOR of V;
reserve z,z1,z2 for Complex;

theorem
  z <> 0 & z * v = z * u implies v = u
proof
  assume that
A1: z <> 0 and
A2: z * v = z * u;
  0.V = z * v - z * u by A2,RLVECT_1:15
    .= z * (v - u) by Th9;
  then v - u = 0.V by A1,Th2;
  hence thesis by RLVECT_1:21;
end;
