reserve x,y,z for boolean object;
reserve i,j,k for Nat;
reserve n for non zero Nat;
reserve x,y,z1,z2 for Tuple of n, BOOLEAN;

theorem
  for z1,z2 being Tuple of n,BOOLEAN st z1,z2 are_summable holds Absval(
  z1+z2) = Absval(z1) + Absval(z2)
proof
  let z1,z2 be Tuple of n,BOOLEAN;
  assume z1,z2 are_summable;
  then add_ovfl(z1,z2) = FALSE;
  then IFEQ(add_ovfl(z1,z2),FALSE,0,2 to_power (n))=0 by FUNCOP_1:def 8;
  hence
  Absval(z1+z2) = Absval(z1+z2) + IFEQ(add_ovfl(z1,z2),FALSE,0,2 to_power (n))
    .= Absval(z1) + Absval(z2) by Th21;
end;
