reserve D for non empty set,
  i,j,k,l for Nat,
  n for Nat,
  x for set,
  a,b,c,r,r1,r2 for Real,
  p,q for FinSequence of REAL,
  MR,MR1 for Matrix of REAL;

theorem Th18:
  for M being Matrix of D holds for i st i in dom M holds dom(M.i)
  = Seg width M
proof
  let M be Matrix of D;
  let i;
  assume i in dom M;
  hence dom(M.i) = dom Line(M,i) by MATRIX_0:60
    .= Seg len Line(M,i) by FINSEQ_1:def 3
    .= Seg width M by MATRIX_0:def 7;
end;
