reserve i1 for Element of INT;
reserve j1,j2,j3 for Integer;
reserve p,s,k,n for Nat;
reserve x,y,xp,yp for set;
reserve G for Group;
reserve a,b for Element of G;
reserve F for FinSequence of G;
reserve I for FinSequence of INT;

theorem
  for G being strict finite Group st card G = p & p is prime holds for H
  being strict Subgroup of G holds H = (1).G or H = G
proof
  let G be strict finite Group;
  assume that
A1: card G = p and
A2: p is prime;
  let H be strict Subgroup of G;
  card H divides p by A1,GROUP_2:148;
  then card H = 1 or card H = p by A2,INT_2:def 4;
  hence thesis by A1,GROUP_2:70,73;
end;
