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

theorem Th24:
  for R being Relation, a,b being object st R reduces a,b
    holds R~ reduces b,a
proof
  let R be Relation, a,b be object;
  given p being RedSequence of R such that
A1: p.1 = a and
A2: p.len p = b;
  reconsider q = Rev p as RedSequence of R~ by Th9;
  take q;
  1 in dom q by FINSEQ_5:6;
  hence q.1 = p.(len p-1+1) by FINSEQ_5:def 3
    .= b by A2;
  len q in dom q & len q = len p by FINSEQ_5:6,def 3;
  hence q.(len q) = p.(len p-len p+1) by FINSEQ_5:def 3
    .= a by A1;
end;
