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 Th69:
  for p being FinSequence of 1-tuples_on REAL st len p = 3 holds
  F2M M2F p = p
  proof
    let p be FinSequence of 1-tuples_on REAL;
    assume
A1: len p = 3;
    set q = M2F p;
    q = <* (p.1).1, (p.2).1, (p.3).1 *> by A1,DEF2;
    then len q = 3 & q.1 = (p.1).1 & q.2 = (p.2).1 &
      q.3 = (p.3).1 by FINSEQ_1:45;
    then F2M q = <* <*(p.1).1*>, <*(p.2).1*> , <*(p.3).1*> *> by DEF1;
    hence thesis by A1,Th68;
  end;
