reserve x,y,z for set;

theorem Th39:
  for S being non void Signature for X being ManySortedSet of the
  carrier of S holds Free(S, X) is feasible free
proof
  let S be non void Signature;
  let X be ManySortedSet of the carrier of S;
  set Y = X (\/) ((the carrier of S) --> {0});
  consider A being MSSubset of FreeMSA Y such that
A1: Free(S, X) = GenMSAlg A and
A2: A = (Reverse Y)"" X by Def1;
  thus Free(S, X) is feasible by A1;
  A is ManySortedSubset of FreeGen Y by A2,EQUATION:8;
  then A c= FreeGen Y by PBOOLE:def 18;
  hence thesis by A1,EQUATION:28;
end;
