reserve a,b,c,d,m,x,n,j,k,l for Nat,
  t,u,v,z for Integer,
  f,F for FinSequence of NAT;
reserve p,q,r,s for real number;
reserve a,b,c,d,m,x,n,k,l for Nat,
  t,z for Integer,
  f,F,G for FinSequence of REAL;
reserve q,r,s for real number;
reserve D for set;

theorem
  not 7 divides a implies 7 divides a|^6 - 1
  proof
    assume not 7 divides a; then
    A1: not a gcd 7 = 7 by INT_2:def 2;
    7 divides a|^(6+1) - a by NAT_4:26,Th58; then
    7 divides a|^6*a - a by NEWTON:6; then
    7 divides a*(a|^6 - 1);
    hence thesis by A1,NAT_4:26,PEPIN:2,INT_2:25;
  end;
