
theorem Th6:
  for X be set, P being a_partition of X, f being FinSequence of X
  ex p being FinSequence of P st f in product p
proof
  let X be set, P be a_partition of X, f be FinSequence of X;
A1: rng f c= X;
  union P = X by EQREL_1:def 4;
  then consider p being Function such that
A2: dom p = dom f and
A3: rng p c= P and
A4: f in product p by A1,Th5;
  dom p = Seg len f by A2,FINSEQ_1:def 3;
  then p is FinSequence by FINSEQ_1:def 2;
  then p is FinSequence of P by A3,FINSEQ_1:def 4;
  hence thesis by A4;
end;
