reserve a,b,c,d,e,f for Real,
        k,m for Nat,
        D for non empty set,
        V for non trivial RealLinearSpace,
        u,v,w for Element of V,
        p,q,r for Element of ProjectiveSpace(V);
reserve o,p,q,r,s,t for Point of TOP-REAL 3,
        M for Matrix of 3,F_Real;
reserve pf for FinSequence of D;
reserve PQR for Matrix of 3,F_Real;

theorem
  <*<e1>*>@ = F2M <e1> & <*<e2>*>@ = F2M <e2> & <*<e3>*>@ = F2M <e3>
  proof
    len <e1> = 3 & <e1>.1 = 1 & <e1>.2 = 0 & <e1>.3 = 0
      by EUCLID_8:def 1,FINSEQ_1:45;
    hence <*<e1>*>@ = F2M <e1> by DEF1,Th57;
    len <e2> = 3 & <e2>.1 = 0 & <e2>.2 = 1 & <e2>.3 = 0
      by EUCLID_8:def 2,FINSEQ_1:45;
    hence <*<e2>*>@ = F2M <e2> by DEF1,Th57;
    len <e3> = 3 & <e3>.1 = 0 & <e3>.2 = 0 & <e3>.3 = 1
      by EUCLID_8:def 3,FINSEQ_1:45;
    hence <*<e3>*>@ = F2M <e3> by DEF1,Th57;
  end;
