let n be non zero Nat; :: thesis: for p being Prime st p |-count n <> 0 holds
(SqFactors n) . p = p |^ ((p |-count n) div 2)
let p be Prime; :: thesis: ( p |-count n <> 0 implies (SqFactors n) . p = p |^ ((p |-count n) div 2) )
assume p |-count n <> 0 ; :: thesis: (SqFactors n) . p = p |^ ((p |-count n) div 2)
then (pfexp n) . p <> 0 by NAT_3:def 8;
then p in support (pfexp n) by PRE_POLY:def 7;
hence (SqFactors n) . p = p |^ ((p |-count n) div 2) by SqDef; :: thesis: verum