
theorem Th16:
  for S1 being non void non empty ManySortedSign, S2 being non
empty ManySortedSign st S1 tolerates S2 for o1 being OperSymbol of S1, o being
  OperSymbol of S1+*S2 st o1 = o holds the_arity_of o = the_arity_of o1 &
  the_result_sort_of o = the_result_sort_of o1
proof
  let S1 be non void non empty ManySortedSign, S2 be non empty ManySortedSign
  such that
A1: the Arity of S1 tolerates the Arity of S2 and
A2: the ResultSort of S1 tolerates the ResultSort of S2;
  let o1 be OperSymbol of S1, o be OperSymbol of S1+*S2;
  assume
A3: o1 = o;
A4: dom the Arity of S1 = the carrier' of S1 by FUNCT_2:def 1;
  the Arity of S1+*S2 = (the Arity of S1)+*(the Arity of S2) by Def2;
  hence the_arity_of o = the_arity_of o1 by A1,A3,A4,FUNCT_4:15;
A5: dom the ResultSort of S1 = the carrier' of S1 by FUNCT_2:def 1;
  the ResultSort of S1+*S2 = (the ResultSort of S1)+*(the ResultSort of S2
  ) by Def2;
  hence thesis by A2,A3,A5,FUNCT_4:15;
end;
