src/HOL/Hyperreal/Transcendental.thy
changeset 23127 56ee8105c002
parent 23115 4615b2078592
child 23176 40a760921d94
equal deleted inserted replaced
23126:93f8cb025afd 23127:56ee8105c002
   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