reserve S for OrderSortedSign;
reserve S for OrderSortedSign,
  X for ManySortedSet of S,
  o for OperSymbol of S ,
  b for Element of ([:the carrier' of S,{the carrier of S}:] \/ Union (coprod X
  ))*;
reserve x for set;

theorem Th39:
  for S be locally_directed OrderSortedSign, X be non-empty
  ManySortedSet of S holds FreeOSA(X) is osfree
proof
  let S be locally_directed OrderSortedSign, X be non-empty ManySortedSet of S;
  take OSFreeGen(X);
  thus thesis by Th38;
end;
