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
      non empty addLoopStr
  for z0,z1,z2,z3 being Element of L holds
  <%z0,z1%> - <%z2,z3%> = <%z0-z2,z1-z3%>
  proof
    let L be add-associative right_zeroed right_complementable
      non empty addLoopStr;
    let z0,z1,z2,z3 be Element of L;
    thus <%z0,z1%> - <%z2,z3%> = <%z0,z1%> + <%-z2,-z3%> by Th31
    .= <%z0-z2,z1-z3%> by Th28;
  end;
