reserve i, j, k, l, m, n, t for Nat;

theorem
  i in Seg n implies n -' i + 1 in Seg n
proof
A1: 1 <= n -' i + 1 by NAT_1:11;
  assume
A2: i in Seg n;
  then 1 <= i by FINSEQ_1:1;
  then n - i <= n - 1 by XREAL_1:13;
  then
A3: n - i + 1 <= n by XREAL_1:19;
  i <= n by A2,FINSEQ_1:1;
  then n -' i + 1 <= n by A3,XREAL_1:233;
  hence thesis by A1,FINSEQ_1:1;
end;
