reserve a,b,c,h for Integer;
reserve k,m,n for Nat;
reserve i,j,z for Integer;
reserve p for Prime;

theorem Th22:
  for a,b being object, f being FinSequence holds
  n in dom f implies n+2 in dom (<*a,b*>^f)
  proof
    let a,b be object, f be FinSequence such that
A1: n in dom f;
A2: 1 <= n by A1,FINSEQ_3:25;
A3: n <= len f by A1,FINSEQ_3:25;
    set g = <*a,b*>;
    n+0 <= n+2 by XREAL_1:6;
    then
A4: 1 <= n+2 by A2,XXREAL_0:2;
    len g = 2 by FINSEQ_1:44;
    then 2+n <= len g + len f by A3,XREAL_1:6;
    then n+2 in Seg (len g + len f) by A4;
    hence thesis by FINSEQ_1:def 7;
  end;
