reserve a,b,c,h for Integer;
reserve k,m,n for Nat;
reserve i,j,z for Integer;
reserve p for Prime;

theorem Th39:
  h <> 0 implies PrimeDivisors>3(h) c= Seg |.h.|
  proof
    assume
A1: h <> 0;
    let x be object;
    assume
A2: x in PrimeDivisors>3(h);
    then reconsider x as Element of NAT;
A3: x >= 1 by A2,Th35,XXREAL_0:2;
    x divides h by A2,Th36;
    then x <= |.h.| by A1,Th4,NAT_D:7;
    hence thesis by A3;
  end;
