
theorem
  for p being 2_greater Prime,
      a,b being Integer
  st a gcd p = 1 & b gcd p = 1 holds Leg(a*b,p) = Leg(a,p) * Leg(b,p)
proof
  let p be 2_greater Prime,
      a,b be Integer;
  assume A1: a gcd p = 1 & b gcd p = 1;
  thus Leg(a*b,p) = Lege(a*b,p) by Lm4
               .= Lege(a,p) * Lege(b,p) by A1,Def1,INT_5:30
               .= Leg(a,p) * Lege(b,p) by Lm4
               .= Leg(a,p) * Leg(b,p) by Lm4;
end;
