
theorem
  for S1,S2 being non empty ManySortedSign for A1 being non-empty
  MSAlgebra over S1, s1 being Element of product the Sorts of A1 for A2 being
non-empty MSAlgebra over S2, s2 being Element of product the Sorts of A2 st the
Sorts of A1 tolerates the Sorts of A2 holds s1+*s2 in product the Sorts of A1+*
  A2
proof
  let S1,S2 be non empty ManySortedSign;
  let A1 be non-empty MSAlgebra over S1;
  let s1 be Element of product ((the Sorts of A1) qua non-empty ManySortedSet
  of the carrier of S1);
  let A2 be non-empty MSAlgebra over S2;
  let s2 be Element of product ((the Sorts of A2) qua non-empty ManySortedSet
  of the carrier of S2);
  assume the Sorts of A1 tolerates the Sorts of A2;
  then the Sorts of A1+*A2 = (the Sorts of A1)+*the Sorts of A2 by Def4;
  hence thesis by CARD_3:97;
end;
