reserve x,y for object,X,Y for set,
  D for non empty set,
  i,j,k,l,m,n,m9,n9 for Nat,
  i0,j0,n0,m0 for non zero Nat,
  K for Field,
  a,b for Element of K,
  p for FinSequence of K,
  M for Matrix of n,K;
reserve A for (Matrix of D),
  A9 for Matrix of n9,m9,D,
  M9 for Matrix of n9, m9,K,
  nt,nt1,nt2 for Element of n-tuples_on NAT,
  mt,mt1 for Element of m -tuples_on NAT,
  M for Matrix of K;
reserve P,P1,P2,Q,Q1,Q2 for without_zero finite Subset of NAT;

theorem Th60:
  for F be FinSequence of D,i,P st not i in P & [:P,Q:] c= Indices A9
  holds Segm(A9,P,Q) = Segm(RLine(A9,i,F),P,Q)
proof
  let F be FinSequence of D,i,P such that
A1: not i in P and
A2: [:P,Q:] c= Indices A9;
  rng Sgm Q=Q & rng Sgm P=P by FINSEQ_1:def 14;
  hence thesis by A1,A2,Th38;
end;
