src/HOL/Real_Vector_Spaces.thy
changeset 62131 1baed43f453e
parent 62102 877463945ce9
child 62347 2230b7047376
equal deleted inserted replaced
62128:3201ddb00097 62131:1baed43f453e
   311   "y \<noteq> 0 \<Longrightarrow> of_real (x / y) =
   311   "y \<noteq> 0 \<Longrightarrow> of_real (x / y) =
   312    (of_real x / of_real y :: 'a::real_field)"
   312    (of_real x / of_real y :: 'a::real_field)"
   313 by (simp add: divide_inverse nonzero_of_real_inverse)
   313 by (simp add: divide_inverse nonzero_of_real_inverse)
   314 
   314 
   315 lemma of_real_divide [simp]:
   315 lemma of_real_divide [simp]:
   316   "of_real (x / y) =
   316   "of_real (x / y) = (of_real x / of_real y :: 'a::real_div_algebra)"
   317    (of_real x / of_real y :: 'a::{real_field, field})"
       
   318 by (simp add: divide_inverse)
   317 by (simp add: divide_inverse)
   319 
   318 
   320 lemma of_real_power [simp]:
   319 lemma of_real_power [simp]:
   321   "of_real (x ^ n) = (of_real x :: 'a::{real_algebra_1}) ^ n"
   320   "of_real (x ^ n) = (of_real x :: 'a::{real_algebra_1}) ^ n"
   322 by (induct n) simp_all
   321 by (induct n) simp_all