
theorem Th15:
  for S be Function,L be FinSequence of NAT st S is disjoint_valued &
  dom S = dom L & for i be Nat st i in dom S holds S.i is finite &
  L.i = card (S.i) holds Union S is finite & card Union S = Sum L
proof
  let S be Function,L be FinSequence of NAT;
A1: len L is Element of NAT;
  assume S is disjoint_valued & dom S = dom L & for i be Nat st i in dom S
  holds S.i is finite & L.i = card (S.i);
  hence thesis by A1,Lm2;
end;
