 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
  for n1,n2 being Element of NAT, m1,m2 being Element of <NAT,+,0> st
    n1 = m1 & n2 = m2 holds m1*m2 = n1+n2
proof
  op(<NAT,+,0>) = op(<NAT,+>) by Th18;
  then <NAT,+,0> is SubStr of <NAT,+> qua SubStr of <REAL,+> by Def23;
  hence thesis by Th39;
end;
