let R be Ring; :: thesis: for S being R -homomorphic Ring
for h being Homomorphism of R,S
for F being FinSequence of R
for a being Element of R holds h . (Product (<*a*> ^ F)) = (h . a) * (h . (Product F))
let S be R -homomorphic Ring; :: thesis: for h being Homomorphism of R,S
for F being FinSequence of R
for a being Element of R holds h . (Product (<*a*> ^ F)) = (h . a) * (h . (Product F))
let h be Homomorphism of R,S; :: thesis: for F being FinSequence of R
for a being Element of R holds h . (Product (<*a*> ^ F)) = (h . a) * (h . (Product F))
let F be FinSequence of R; :: thesis: for a being Element of R holds h . (Product (<*a*> ^ F)) = (h . a) * (h . (Product F))
let a be Element of R; :: thesis: h . (Product (<*a*> ^ F)) = (h . a) * (h . (Product F))
thus h . (Product (<*a*> ^ F)) = h . ((Product <*a*>) * (Product F)) by GROUP_4:5
.= (h . (Product <*a*>)) * (h . (Product F)) by GROUP_6:def 6
.= (h . a) * (h . (Product F)) by GROUP_4:9 ; :: thesis: verum