
theorem Th14:
  for S1 being non empty ManySortedSign, S2 being non void non
empty ManySortedSign for o2 being OperSymbol of S2, o being OperSymbol of S1+*
  S2 st o2 = o holds the_arity_of o = the_arity_of o2 & the_result_sort_of o =
  the_result_sort_of o2
proof
  let S1 be non empty ManySortedSign;
  let S2 be non void non empty ManySortedSign;
  let o2 be OperSymbol of S2, o be OperSymbol of S1+*S2;
  assume
A1: o2 = o;
A2: dom the Arity of S2 = the carrier' of S2 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 o2 by A1,A2,FUNCT_4:13;
A3: dom the ResultSort of S2 = the carrier' of S2 by FUNCT_2:def 1;
  the ResultSort of S1+*S2 = (the ResultSort of S1)+*(the ResultSort of S2
  ) by Def2;
  hence thesis by A1,A3,FUNCT_4:13;
end;
