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,z4,z5 being Element of L holds
  <%z0,z1,z2%> - <%z3,z4,z5%> = <%z0-z3,z1-z4,z2-z5%>
  proof
    let L be add-associative right_zeroed right_complementable
      non empty addLoopStr;
    let z0,z1,z2,z3,z4,z5 be Element of L;
    thus <%z0,z1,z2%> - <%z3,z4,z5%> = <%z0,z1,z2%> + <%-z3,-z4,-z5%> by Th32
    .= <%z0-z3,z1-z4,z2-z5%> by Th29;
  end;
