
theorem Th24:
  for p be Prime,
      a be Integer
  holds Leg(a,p) = 1 or Leg(a,p) = 0 or Leg(a,p) = -1
proof
  let p be Prime;
  let a be Integer;
assume A1: Leg(a,p) <> 1 & Leg(a,p) <> 0;
a gcd p = 1
  proof
  a gcd p = 1 or a gcd p = p by INT_2:def 4,INT_2:21;
  hence thesis by A1,Def4,INT_2:21;
  end;
hence Leg(a,p) = -1 by A1,Def4;
end;
