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

theorem Th51:
  for n being non zero Nat holds
  PrimeDivisorsFS(n) = sort_a canFS support pfexp n
  proof
    let n be non zero Nat;
    set X = PrimeDivisors(n);
    set P = PrimeDivisorsFS(n);
    set f = canFS support pfexp n;
    set S = sort_a f;
A1: P is FinSequence of REAL by FINSEQ_1:106;
    f is FinSequence of REAL by FINSEQ_1:106;
    then
A2: S is one-to-one by EUCLID_7:13;
A3: rng P = X by FINSEQ_1:def 14;
    rng f = support pfexp n by FUNCT_2:def 3;
    then rng S = support pfexp n by CLASSES1:75,RFINSEQ2:def 6;
    hence thesis by A1,A2,A3,Th48,INTEGRA3:6;
  end;
