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 Th62:
  len pf = 3 implies Line(<*pf*>@,1) = <* pf.1 *> &
  Line(<*pf*>@,2) = <* pf.2 *> & Line(<*pf*>@,3) = <* pf.3 *>
  proof
    assume
A1: len pf = 3;
A3: width <*pf*> = 3 by A1,Th61;
    1 in Seg width <*pf*> by A3,FINSEQ_1:1;
    hence Line(<*pf*>@,1) = Col(<*pf*>,1) by MATRIX_0:59
                         .= <* pf.1 *> by A1,Th51;
    2 in Seg width <*pf*> by A3,FINSEQ_1:1;
    hence Line(<*pf*>@,2) = Col(<*pf*>,2) by MATRIX_0:59
                         .= <* pf.2 *> by A1,Th51;
    3 in Seg width <*pf*> by A3,FINSEQ_1:1;
    hence Line(<*pf*>@,3) = Col(<*pf*>,3) by MATRIX_0:59
                         .= <* pf.3 *> by A1,Th51;
  end;
