reserve n,i,k,m for Nat;

theorem
  for n,k being Nat holds n < k implies n <= k-1
proof
  let n,k be Nat;
  assume n<k;
  then n+1<=k by NAT_1:13;
  then n+1-1<=k-1 by XREAL_1:9;
  hence thesis;
end;
