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 . (Sum (F ^ <*a*>)) = (h . (Sum F)) + (h . a)
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 . (Sum (F ^ <*a*>)) = (h . (Sum F)) + (h . a)
let h be Homomorphism of R,S; :: thesis: for F being FinSequence of R
for a being Element of R holds h . (Sum (F ^ <*a*>)) = (h . (Sum F)) + (h . a)
let F be FinSequence of R; :: thesis: for a being Element of R holds h . (Sum (F ^ <*a*>)) = (h . (Sum F)) + (h . a)
let a be Element of R; :: thesis: h . (Sum (F ^ <*a*>)) = (h . (Sum F)) + (h . a)
thus h . (Sum (F ^ <*a*>)) = h . ((Sum F) + (Sum <*a*>)) by RLVECT_1:41
.= (h . (Sum F)) + (h . (Sum <*a*>)) by VECTSP_1:def 20
.= (h . (Sum F)) + (h . a) by RLVECT_1:44 ; :: thesis: verum