reserve i,j,k,n for Nat,
  D for non empty set,
  f, g for FinSequence of D;

theorem Th3:
  n in dom f implies ex k st k in dom Rev f & n+k = len f+1 & f/.n = (Rev f)/.k
proof
  assume
A1: n in dom f;
  take k = len f+1-'n;
  1 <= n by A1,FINSEQ_3:25;
  then k+1 <= k+n by XREAL_1:6;
  then
A2: k+1-'1 <= k+n -'1 by NAT_D:42;
A3: n <= len f by A1,FINSEQ_3:25;
  then n+1 <= len f+1 by XREAL_1:6;
  then
A4: 1 <= k by NAT_D:55;
  n <= len f+1 by A3,XREAL_1:145;
  then
A5: k+n = len f+1 by XREAL_1:235;
  then k+n-'1 = len f by NAT_D:34;
  then k <= len f by A2,NAT_D:34;
  then k in dom f by A4,FINSEQ_3:25;
  hence thesis by A1,A5,FINSEQ_5:57,66;
end;
