theorem
  a <> 0 implies a /// (A/\B) = (a///A) /\ (a///B)
proof
  assume
A1: a <> 0;
  thus a /// (A/\B) = a ** ((A"")/\(B"")) by Th33
    .= (a**(A"")) /\ (a**(B"")) by A1,Th198
    .= (a///A) /\ (a///B);
end;
