
theorem Th2:
  for I being non empty set for i be Element of I for A being
  non-Trivial-yielding 1-sorted-yielding ManySortedSet of I holds A.i is non
  trivial
proof
  let I be non empty set;
  let i be Element of I;
  let A be non-Trivial-yielding 1-sorted-yielding ManySortedSet of I;
  dom A = I by PARTFUN1:def 2;
  then A.i in rng A by FUNCT_1:3;
  hence thesis by PENCIL_1:def 17;
end;
