reserve r1,r2 for Real;
reserve n,i,i1,i2,j for Nat;
reserve D for non empty set;
reserve f for FinSequence of D;

theorem Th15:
  for g being FinSequence of TOP-REAL 2, p1,p2 being Point of
  TOP-REAL 2 st g is_S-Seq_joining p1,p2 holds Rev g is_S-Seq_joining p2,p1
proof
  let g be FinSequence of TOP-REAL 2, p1,p2 be Point of TOP-REAL 2;
  assume that
A1: g is being_S-Seq and
A2: g.1=p1 and
A3: g.len g=p2;
  thus Rev g is being_S-Seq by A1;
  thus (Rev g).1 = p2 by A3,FINSEQ_5:62;
  dom g = dom Rev g by FINSEQ_5:57;
  hence (Rev g).len Rev g = (Rev g).len g by FINSEQ_3:29
    .= p1 by A2,FINSEQ_5:62;
end;
