let n be non zero Nat; :: thesis: for p being Prime st p |-count n <> 0 holds
(Bnumber_of_divisors n) . p = (p |-count n) + 1
let p be Prime; :: thesis: ( p |-count n <> 0 implies (Bnumber_of_divisors n) . p = (p |-count n) + 1 )
assume p |-count n <> 0 ; :: thesis: (Bnumber_of_divisors n) . p = (p |-count n) + 1
then (pfexp n) . p <> 0 by NAT_3:def 8;
then p in support (pfexp n) by PRE_POLY:def 7;
hence (Bnumber_of_divisors n) . p = (p |-count n) + 1 by BDef; :: thesis: verum