theorem Th11:
  id V is with_eigenvalues & 1_K is eigenvalue of id V & for v
  holds v is eigenvector of id V,1_K
proof
  thus
A1: id V is with_eigenvalues by Lm2;
  ex v st v<>0.V & id V.v=1_K*v by Lm2;
  hence
A2: 1_K is eigenvalue of id V by A1,Def2;
  let w;
  id V.w = w
    .= 1_K*w;
  hence thesis by A1,A2,Def3;
end;
