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

theorem Th40:
  h <> 0 implies
  for n being Nat st n in dom Sgm PrimeDivisors>3(h) holds
  (Sgm PrimeDivisors>3(h)).n > 3
  proof
    set X = PrimeDivisors>3(h);
    set f = Sgm X;
    assume
A1: h <> 0;
    let n be Nat;
    assume n in dom f;
    then
A2: f.n in rng f by FUNCT_1:def 3;
    rng f = X by A1,FINSEQ_1:def 14;
    hence thesis by A2,Th35;
  end;
