
theorem Th49:
  for S1,S2 being unsplit non empty ManySortedSign holds S1+*S2 is unsplit
proof
  let S1,S2 be unsplit non empty ManySortedSign;
  set S = S1+*S2;
A1: the ResultSort of S = (the ResultSort of S1)+*the ResultSort of S2 by Def2;
A2: the ResultSort of S1 = id the carrier' of S1 by Def7;
A3: the ResultSort of S2 = id the carrier' of S2 by Def7;
  the carrier' of S = (the carrier' of S1) \/ the carrier' of S2 by Def2;
  hence the ResultSort of S = id the carrier' of S by A1,A2,A3,FUNCT_4:22;
end;
