let L be non empty right_complementable Abelian add-associative right_zeroed well-unital distributive commutative doubleLoopStr ; :: thesis: for p being Polynomial of L holds p `^ 1 = p
let p be Polynomial of L; :: thesis: p `^ 1 = p
reconsider p1 = p as Element of (Polynom-Ring L) by POLYNOM3:def 10;
thus p `^ 1 = (power (Polynom-Ring L)) . (p1,(0 + 1))
.= ((power (Polynom-Ring L)) . (p1,0)) * p1 by GROUP_1:def 7
.= (1_ (Polynom-Ring L)) * p1 by GROUP_1:def 7
.= p ; :: thesis: verum