
theorem Th1:
  for I,J being set st J in Fin I holds
  ex p being FinSequence of I st J = rng p & p is one-to-one
  proof
    let I, J be set such that
A1: J in Fin I;
    consider p be FinSequence such that
A2: J = rng p & p is one-to-one by A1,FINSEQ_4:58;
    rng p c= I by A1,A2,FINSUB_1:def 5;
    then reconsider p as FinSequence of I by FINSEQ_1:def 4;
    take p;
    thus thesis by A2;
end;
