let L be non empty right_complementable Abelian add-associative right_zeroed commutative well-unital distributive doubleLoopStr ; :: thesis: for p being Polynomial of L
for n being Element of NAT holds p `^ (n + 1) = (p `^ n) *' p
let p be Polynomial of L; :: thesis: for n being Element of NAT holds p `^ (n + 1) = (p `^ n) *' p
let n be Element of NAT ; :: thesis: p `^ (n + 1) = (p `^ n) *' p
reconsider p1 = p as Element of (Polynom-Ring L) by POLYNOM3:def 12;
thus p `^ (n + 1) = ((power (Polynom-Ring L)) . p1,n) * p1 by GROUP_1:def 8
.= (p `^ n) *' p by POLYNOM3:def 12 ; :: thesis: verum