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