
theorem Th7:
  for n,p being Nat holds p > 0 & n divides p & n <> 1 & n <> p
  implies 1 < n & n < p
proof
  let n,p be Nat;
  assume
A1: p>0 & n divides p;
  assume
A2: n <> 1;
  assume
A3: n <> p;
  n <> 0 by A1,INT_2:3;
  hence 1 < n by A2,NAT_1:25;
  n <= p by A1,NAT_D:7;
  hence thesis by A3,XXREAL_0:1;
end;
