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 Th70:
  for p being FinSequence of REAL st len p = 3 holds M2F F2M p = p
  proof
    let p be FinSequence of REAL;
    assume
A1: len p = 3;
    set q = F2M p;
    q = <* <*p.1*>, <*p.2*> , <*p.3*> *> by A1,DEF1; then
A2: len q = 3 & q.1 = <*p.1*> & q.2 = <*p.2*> & q.3 = <*p.3*> by FINSEQ_1:45;
    then (q.1).1 = p.1 & (q.2).1 = p.2 & (q.3).1 = p.3; then
    M2F q = <*p.1,p.2,p.3*> by A2,DEF2
         .= p by A1,FINSEQ_1:45;
    hence thesis;
  end;
