reserve i,j,k,n,m,l,s,t for Nat;
reserve a,b for Real;
reserve F for real-valued FinSequence;
reserve z for Complex;
reserve x,y for Complex;
reserve r,s,t for natural Number;

theorem Th35:
  l <> 0 implies l divides l!
proof
  assume l<>0;
  then consider n being Nat such that
A1: l = n+1 by NAT_1:6;
  reconsider n as Element of NAT by ORDINAL1:def 12;
  (n+1)! = (n+1) * (n!) by Th15;
  hence thesis by A1,NAT_D:def 3;
end;
