reserve p,q,r for FinSequence,
  x,y for object;

theorem Th9:
  for R being Relation, p being RedSequence of R holds
    Rev p is RedSequence of R~
proof
  let R be Relation, p be RedSequence of R;
  len p > 0;
  hence len Rev p > 0 by FINSEQ_5:def 3;
  let i be Nat;
  assume that
A1: i in dom Rev p and
A2: i+1 in dom Rev p;
A3: len Rev p = len p by FINSEQ_5:def 3;
  then
A4: dom Rev p = Seg len p by FINSEQ_1:def 3;
  i+1 <= len p by A3,A2,Lm1;
  then reconsider k = len p-(i+1)+1 as Nat by FINSEQ_5:1;
A5: dom p = Seg len p by FINSEQ_1:def 3;
  then
A6: k in dom p by A4,A2,FINSEQ_5:2;
  k = len p-i;
  then k+1 in dom p by A4,A5,A1,FINSEQ_5:2;
  then
A7: [p.k, p.(k+1)] in R by A6,Def2;
  (Rev p).i = p.(len p-i+1) & (Rev p).(i+1) = p.(len p-(i+1)+1) by A1,A2,
FINSEQ_5:def 3;
  hence thesis by A7,RELAT_1:def 7;
end;
