 reserve x,y,X,Y for set;
reserve G for non empty multMagma,
  D for set,
  a,b,c,r,l for Element of G;
reserve M for non empty multLoopStr;
reserve H for non empty SubStr of G,
  N for non empty MonoidalSubStr of G;

theorem
  x is Element of <NAT,+,0> iff x is Element of NAT
proof
  carr(<NAT,+,0>) = carr(<NAT,+>) by Th18
    .= NAT by Def27;
  hence thesis;
end;
