
theorem Th3:
  for S1,S2,S3 being non empty ManySortedSign st S1 tolerates S2 &
  S2 tolerates S3 & S3 tolerates S1 holds S1+*S2 tolerates S3
proof
  let S1,S2,S3 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 and
A3: the Arity of S2 tolerates the Arity of S3 and
A4: the ResultSort of S2 tolerates the ResultSort of S3 and
A5: the Arity of S3 tolerates the Arity of S1 and
A6: the ResultSort of S3 tolerates the ResultSort of S1;
  the Arity of S1+*S2 = (the Arity of S1)+*the Arity of S2 by Def2;
  hence the Arity of S1+*S2 tolerates the Arity of S3 by A1,A3,A5,FUNCT_4:125;
  the ResultSort of S1+*S2 = (the ResultSort of S1)+*the ResultSort of S2
  by Def2;
  hence thesis by A2,A4,A6,FUNCT_4:125;
end;
