reserve P for Subset of TOP-REAL 2,
  f,f1,f2,g for FinSequence of TOP-REAL 2,
  p,p1,p2,q,q1,q2 for Point of TOP-REAL 2,
  r1,r2,r19,r29 for Real,
  i,j,k,n for Nat;

theorem Th28:
  f is unfolded implies Rev f is unfolded
proof
  assume
A1: f is unfolded;
A2: dom f = Seg len f by FINSEQ_1:def 3;
  let i be Nat such that
A3: 1 <= i and
A4: i + 2 <= len Rev f;
A5: len Rev f = len f by FINSEQ_5:def 3;
  then
A6: i+1 in dom f by A3,A4,SEQ_4:135;
  i+1 <= i+1+1 by NAT_1:11;
  then reconsider j9 = len f - (i+1) as Element of NAT by A4,A5,INT_1:5
,XXREAL_0:2;
  i <= i+2 by NAT_1:11;
  then reconsider j = len f - i as Element of NAT by A4,A5,INT_1:5,XXREAL_0:2;
A7: j9+(i+1) = len f;
  i in dom f by A3,A4,A5,SEQ_4:135;
  then j + 1 in dom f by A2,FINSEQ_5:2;
  then
A8: j9+2 <= len f by FINSEQ_3:25;
A9: j + (i+1) = len f + 1;
  i+(1+1) = i+1+1;
  then
A10: 1 <= j9 by A4,A5,XREAL_1:19;
  j+i = len f;
  hence LSeg(Rev f,i) /\ LSeg(Rev f,i+1) = LSeg(f,j) /\ LSeg(Rev f,i+1) by Th2
    .= LSeg(f,j9+1) /\ LSeg(f,j9) by A7,Th2
    .= {f/.(j9+1)} by A1,A10,A8
    .= {(Rev f)/.(i+1)} by A9,A2,A6,FINSEQ_5:2,66;
end;
