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

theorem Th5:
  for f being FinSequence st n <> 0 & f in Permutations n holds Rev
  f in Permutations n
proof
  let f be FinSequence;
  assume that
A1: n <> 0 and
A2: f in Permutations n;
A3: f is Permutation of Seg n by A2,MATRIX_1:def 12;
  dom f = dom Rev f by FINSEQ_5:57;
  then
A4: dom Rev f = Seg n by A1,A3,FUNCT_2:def 1;
A5: rng f = rng Rev f by FINSEQ_5:57;
  then rng Rev f = Seg n by A3,FUNCT_2:def 3;
  then reconsider g = Rev f as FinSequence-like Function of Seg n,Seg n by A4,
FUNCT_2:2;
  rng f = Seg n by A3,FUNCT_2:def 3;
  then g is onto by A5,FUNCT_2:def 3;
  hence thesis by A3,MATRIX_1:def 12;
end;
