src/HOL/Hyperreal/HTranscendental.thy
changeset 17332 4910cf8c0cd2
parent 17318 bc1c75855f3d
child 19765 dfe940911617
equal deleted inserted replaced
17331:6b8b27894133 17332:4910cf8c0cd2
   129 lemma hypreal_sqrt_hrabs2 [simp]: "!!x. ( *f* sqrt)(x*x) = abs(x)"
   129 lemma hypreal_sqrt_hrabs2 [simp]: "!!x. ( *f* sqrt)(x*x) = abs(x)"
   130 by (transfer, simp)
   130 by (transfer, simp)
   131 
   131 
   132 lemma hypreal_sqrt_hyperpow_hrabs [simp]:
   132 lemma hypreal_sqrt_hyperpow_hrabs [simp]:
   133      "!!x. ( *f* sqrt)(x pow (hypnat_of_nat 2)) = abs(x)"
   133      "!!x. ( *f* sqrt)(x pow (hypnat_of_nat 2)) = abs(x)"
   134 by (unfold hyperpow_def, transfer, simp)
   134 by (transfer, simp)
   135 
   135 
   136 lemma star_sqrt_HFinite: "\<lbrakk>x \<in> HFinite; 0 \<le> x\<rbrakk> \<Longrightarrow> ( *f* sqrt) x \<in> HFinite"
   136 lemma star_sqrt_HFinite: "\<lbrakk>x \<in> HFinite; 0 \<le> x\<rbrakk> \<Longrightarrow> ( *f* sqrt) x \<in> HFinite"
   137 apply (rule HFinite_square_iff [THEN iffD1])
   137 apply (rule HFinite_square_iff [THEN iffD1])
   138 apply (simp only: hypreal_sqrt_mult_distrib2 [symmetric], simp) 
   138 apply (simp only: hypreal_sqrt_mult_distrib2 [symmetric], simp) 
   139 done
   139 done