reserve X for set;
reserve a,b,c,k,m,n for Nat;
reserve i for Integer;
reserve r for Real;
reserve p for Prime;

theorem Th38:
  11 divides 2|^561-2
  proof
    1023 = 11*93;
    then 2|^10,1 are_congruent_mod 11 by Lm10;
    then 2|^10|^56,1|^56 are_congruent_mod 11 by GR_CY_3:34;
    then 2|^560*2|^1,1*2 are_congruent_mod 11 by Lm1119,INT_4:11;
    hence thesis by Lm1121;
  end;
