
theorem Mod22:
  for n being Nat st n mod 11 = 1 & n mod 2 = 1 holds
    n mod 22 = 1
  proof
    let n be Nat;
    assume
A2: n mod 11 = 1 & n mod 2 = 1; then
A3: 11 divides n - 1 & 2 divides n - 1 by PEPIN:8;
a0: n is odd by A2,NAT_2:22; then
    2 * 11 divides n - 1
      by INT_2:30,XPRIMES1:2,11,A3,PEPIN:4; then
B1: (n - 1) mod 22 = 0 by a0,PEPIN:6; then
    n - 1 mod 22 < 22 - 1; then
    (n - 1) + 1 mod 22 = (n - 1) mod 22 + 1 by a0,NAT_D:70;
    hence thesis by B1;
  end;
