reserve x,y,z, X,Y,Z for set,
  n for Element of NAT;
reserve A for set,
  D for non empty set,
  a,b,c,l,r for Element of D,
  o,o9 for BinOp of D,
  f,g,h for Function of A,D;
reserve G for non empty multMagma;
reserve A for non empty set,
  a for Element of A,
  p for FinSequence of A,
  m1,m2 for Multiset of A;

theorem Th37:
  |.<*> A.| = A --> 0
proof
A1: now
    let x be object;
    assume x in A;
    then reconsider a = x as Element of A;
    thus |.<*>A.|.x = card dom ({a}|`{}) by Def7
      .= 0 by CARD_1:27,RELAT_1:38,107;
  end;
  dom |.<*>A.| = A by Th28;
  hence thesis by A1,FUNCOP_1:11;
end;
