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

theorem Th6:
  Permutations 2 = { idseq 2, Rev idseq 2 }
proof
  now
    let p be object;
    assume p in Permutations 2;
    then reconsider q = p as Permutation of Seg 2 by MATRIX_1:def 12;
A1: rng q = Seg 2 by FUNCT_2:def 3;
A2: dom q = Seg 2 by FUNCT_2:52;
    then reconsider q as FinSequence by FINSEQ_1:def 2;
    q = idseq 2 or q = Rev idseq 2 by A1,A2,Th3;
    hence p in {idseq 2, Rev idseq 2} by TARSKI:def 2;
  end;
  then
A3: Permutations 2 c= {idseq 2, Rev idseq 2 } by TARSKI:def 3;
  now
    let x be object;
    assume x in {idseq 2, Rev idseq 2 };
    then x = idseq 2 or x = Rev idseq 2 by TARSKI:def 2;
    hence x in Permutations 2 by Th4,MATRIX_1:def 12;
  end;
  then {idseq 2, Rev idseq 2 } c= Permutations 2 by TARSKI:def 3;
  hence thesis by A3,XBOOLE_0:def 10;
end;
