src/HOL/Decision_Procs/ex/Approximation_Ex.thy
changeset 63931 f17a1c60ac39
parent 63263 c6c95d64607a
child 69597 ff784d5a5bfb
equal deleted inserted replaced
63930:867ca0d92ea2 63931:f17a1c60ac39
    76   using assms by (approximation 20)
    76   using assms by (approximation 20)
    77 
    77 
    78 lemma "x \<in> { 0 .. 1 :: real } \<longrightarrow> x\<^sup>2 \<le> x"
    78 lemma "x \<in> { 0 .. 1 :: real } \<longrightarrow> x\<^sup>2 \<le> x"
    79   by (approximation 30 splitting: x=1 taylor: x = 3)
    79   by (approximation 30 splitting: x=1 taylor: x = 3)
    80 
    80 
    81 approximate "10"
    81 lemma "(n::real) \<in> {32 .. 62} \<Longrightarrow> \<lceil>log 2 (2 * (\<lfloor>n\<rfloor> div 2) + 1)\<rceil> = \<lceil>log 2 (\<lfloor>n\<rfloor> + 1)\<rceil>"
       
    82   unfolding eq_iff
       
    83   by (approximation 20)
       
    84 
       
    85 approximate 10
    82 
    86 
    83 end
    87 end