 reserve n,s for Nat;

theorem Th36:
  for n being odd Nat st s >= 2 holds
    n divides Polygon (s,n)
  proof
    let n be odd Nat;
    assume
A1: s >= 2;
A2: Polygon (s,n) = (n * (s - 2) * (n - 1)) / 2 + n;
A3: s - 0 >= 2 by A1; then
    s - 2 >= 0 by XREAL_1:11; then
A4: n * (s - 2) * (n - 1) in NAT by INT_1:3;
    reconsider k = (n * (s - 2) * (n - 1)) / 2 as Nat by A4;
A5: s - 2 in NAT by INT_1:3,A3,XREAL_1:11;
    k = n * ((s - 2) * ((n - 1) / 2)); then
    n divides k by NAT_D:def 3,A5;
    hence thesis by A2,NAT_D:8;
  end;
