reserve m,n for Nat;
reserve r for Real;
reserve c for Element of F_Complex;

theorem
  for R being non degenerated Ring, S being non degenerated Subring of R
  for f being monic Polynomial of S
  for g being Polynomial of R st f = g holds
  g is monic
  proof
    let R be non degenerated Ring;
    let S be non degenerated Subring of R;
    let f be monic Polynomial of S;
    let g be Polynomial of R;
    assume f = g;
    hence LC g = LC f by Th9
    .= 1.S by RATFUNC1:def 7
    .= 1.R by C0SP1:def 3;
  end;
