reserve x,y,z for set;

theorem
  for S being non void Signature for X being ManySortedSet of the
  carrier of S holds
  (FreeMSA (X (\/) ((the carrier of S)-->{0})))|
   (S-Terms(X, X (\/) ((the carrier of S)-->{0}))) = Free(S, X)
proof
  let S be non void Signature;
  let X be ManySortedSet of the carrier of S;
  set Y = X (\/) ((the carrier of S)-->{0});
  (FreeMSA Y)|(S-Terms(X, Y)) = MSAlgebra(#S-Terms(X, Y), Opers(FreeMSA Y,
S -Terms(X, Y))#) & ex A being MSSubset of FreeMSA Y st Free(S, X) = GenMSAlg A
  & A = (Reverse Y)""X by Def1,Th21,MSUALG_2:def 15;
  hence thesis by Th24,MSUALG_2:9;
end;
