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 Th60:
  PQR = <*<*p`1,p`2,p`3*>,<*q`1,q`2,q`3*>,<*r`1,r`2,r`3*>*> implies
  Line(PQR,1) = p & Line(PQR,2) = q & Line(PQR,3) = r
  proof
    assume
A1: PQR = <*<*p`1,p`2,p`3*>,<*q`1,q`2,q`3*>,<*r`1,r`2,r`3*>*>;
    1 in Seg 3 by FINSEQ_1:1;
    hence Line(PQR,1) = PQR.1 by MATRIX_0:52
                     .= <*p`1,p`2,p`3*> by A1
                     .= p by EUCLID_5:3;
    2 in Seg 3 by FINSEQ_1:1;
    hence Line(PQR,2) = PQR.2 by MATRIX_0:52
                     .= <*q`1,q`2,q`3*> by A1
                     .= q by EUCLID_5:3;
    3 in Seg 3 by FINSEQ_1:1;
    hence Line(PQR,3) = PQR.3 by MATRIX_0:52
                     .= <*r`1,r`2,r`3*> by A1
                     .= r by EUCLID_5:3;
  end;
