reserve x for set,
  i,j,k,n for Nat,
  K for Field;

theorem Th4:
  Rev idseq n in Permutations n
proof
  reconsider f = idseq n as one-to-one FinSequence-like Function of Seg n, Seg
  n;
  dom f = dom Rev f by FINSEQ_5:57;
  then
A1: dom Rev f = Seg n by RELAT_1:45;
A2: rng idseq n = Seg n by FUNCT_2:def 3;
  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 by MATRIX_1:def 12;
end;
