equal
deleted
inserted
replaced
718 (\<Sum>i=0..Suc n. real (Suc n-i) *# (S x i * S y (Suc n-i))) = |
718 (\<Sum>i=0..Suc n. real (Suc n-i) *# (S x i * S y (Suc n-i))) = |
719 (\<Sum>i=0..Suc n. real (Suc n) *# (S x i * S y (Suc n-i)))" |
719 (\<Sum>i=0..Suc n. real (Suc n) *# (S x i * S y (Suc n-i)))" |
720 by (simp only: setsum_addf [symmetric] scaleR_left_distrib [symmetric] |
720 by (simp only: setsum_addf [symmetric] scaleR_left_distrib [symmetric] |
721 real_of_nat_add [symmetric], simp) |
721 real_of_nat_add [symmetric], simp) |
722 also have "\<dots> = real (Suc n) *# (\<Sum>i=0..Suc n. S x i * S y (Suc n-i))" |
722 also have "\<dots> = real (Suc n) *# (\<Sum>i=0..Suc n. S x i * S y (Suc n-i))" |
723 by (simp only: additive_scaleR_right.setsum) |
723 by (simp only: scaleR_right.setsum) |
724 finally show |
724 finally show |
725 "S (x + y) (Suc n) = (\<Sum>i=0..Suc n. S x i * S y (Suc n - i))" |
725 "S (x + y) (Suc n) = (\<Sum>i=0..Suc n. S x i * S y (Suc n - i))" |
726 by (simp add: scaleR_cancel_left del: setsum_cl_ivl_Suc) |
726 by (simp add: scaleR_cancel_left del: setsum_cl_ivl_Suc) |
727 qed |
727 qed |
728 |
728 |