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

theorem Th26:
  for f being FinSequence st i in dom(f/^n) holds n+i in dom f
proof
  let f be FinSequence;
  assume
A1: i in dom(f/^n);
  per cases;
  suppose
A2: n <= len f;
    i <= len(f/^n) by A1,FINSEQ_3:25;
    then i <= len f - n by A2,RFINSEQ:def 1;
    then
A3: n+i <= len f by XREAL_1:19;
    1 <= i & i <= i+n by A1,FINSEQ_3:25,NAT_1:11;
    then 1 <= i+n by XXREAL_0:2;
    hence thesis by A3,FINSEQ_3:25;
  end;
  suppose
    n > len f;
    then f/^n = {} by RFINSEQ:def 1;
    hence thesis by A1;
  end;
end;
