reserve r,t for Real;
reserve i for Integer;
reserve k,n for Nat;
reserve p for Polynomial of F_Real;
reserve e for Element of F_Real;
reserve L for non empty ZeroStr;
reserve z,z0,z1,z2 for Element of L;

theorem
  for L being add-associative right_zeroed right_complementable distributive
      non degenerated doubleLoopStr
  for p being Polynomial of L holds
  LC p = -LC -p
  proof
    let L be add-associative right_zeroed right_complementable distributive
        non degenerated doubleLoopStr;
    let p be Polynomial of L;
A1: len p = len(-p) by POLYNOM4:8;
A2: dom(-p) = NAT by FUNCT_2:def 1;
    thus LC p = --(p/.(len p-'1))
    .= -((-p)/.(len(-p)-'1)) by A1,A2,VFUNCT_1:def 5
    .= -LC -p;
  end;
