reserve a,b,i,k,m,n for Nat;
reserve s,z for non zero Nat;
reserve r for Real;
reserve c for Complex;
reserve e1,e2,e3,e4,e5 for ExtReal;

theorem Th11:
  for n being Integer holds n mod (m+1) = 0 or ... or n mod (m+1) = m
  proof
    let n be Integer;
    reconsider i = n mod (m+1) as Element of NAT by INT_1:3,INT_1:57;
    take i;
    thus 0 <= i;
    i < m + 1 by INT_1:58;
    hence i <= m by NAT_1:13;
    thus thesis;
  end;
