reserve a,b,i,j,k,l,m,n for Nat;

theorem MATRIX94:
  Rev idseq n is Permutation of (Seg n)
  proof
    reconsider f = idseq n as one-to-one FinSequence-like Function of
      Seg n, Seg n by FINSEQ_2:55;
    A1: dom Rev (idseq n) = dom (idseq n) by FINSEQ_5:57
    .= dom (id (Seg n)) by FINSEQ_2:def 1
    .= Seg n;
    A2: rng idseq n = rng (id (Seg n)) by FINSEQ_2:def 1
    .= Seg n; then
    rng Rev f c= Seg n by FINSEQ_5:57; then
    reconsider
    g = Rev f as FinSequence-like Function of Seg n, Seg n by A1,FUNCT_2:2;
    rng f = rng Rev f by FINSEQ_5:57; then
    g is onto by A2,FUNCT_2:def 3;
  hence thesis;
end;
