
theorem Th10:
  for S being feasible ManySortedSign, T being Subsignature of S
holds the carrier of T c= the carrier of S & the carrier' of T c= the carrier'
  of S
proof
  let S be feasible ManySortedSign, T be Subsignature of S;
  set g = id the carrier' of T;
  id the carrier of T, g form_morphism_between T,S by Def2;
  then rng id the carrier of T c= the carrier of S & rng id the carrier' of T
  c= the carrier' of S;
  hence thesis;
end;
