
theorem Th3:
  for G being non empty ManySortedSign holds SortsWithConstants G
  c= InnerVertices G
proof
  let G be non empty ManySortedSign;
  per cases;
  suppose
    G is void;
    hence thesis by Def1;
  end;
  suppose
A1: G is non void;
    let x be object;
    assume
A2: x in SortsWithConstants G;
    SortsWithConstants G = {v where v is SortSymbol of G:v is
    with_const_op } by A1,Def1;
    then consider x9 being SortSymbol of G such that
A3: x9=x and
A4: x9 is with_const_op by A2;
    ex o being OperSymbol of G st (the Arity of G).o = {} & ( the
    ResultSort of G).o = x9 by A4;
    hence thesis by A1,A3,FUNCT_2:4;
  end;
end;
