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 Th2:
  z * v = 0.V implies z = 0 or v = 0.V
proof
  assume that
A1: z * v = 0.V and
A2: z <> 0;
  thus v = 1r * v by Def5
    .= (z" * z) * v by A2,XCMPLX_0:def 7
    .= z" * 0.V by A1,Def4
    .= 0.V by Th1;
end;
