isabelle: src/HOL/SPARK/Examples/Sqrt/Sqrt.thy@a96320074298 (annotated)

41561 d1318f3c86ba Added new SPARK verification environment. berghofe parents: diff changeset	1	(* Title: HOL/SPARK/Examples/Sqrt/Sqrt.thy
d1318f3c86ba Added new SPARK verification environment. berghofe parents: diff changeset	2	Author: Stefan Berghofer
d1318f3c86ba Added new SPARK verification environment. berghofe parents: diff changeset	3	Copyright: secunet Security Networks AG
d1318f3c86ba Added new SPARK verification environment. berghofe parents: diff changeset	4	*)
d1318f3c86ba Added new SPARK verification environment. berghofe parents: diff changeset	5
d1318f3c86ba Added new SPARK verification environment. berghofe parents: diff changeset	6	theory Sqrt
66992 69673025292e less global theories -- avoid confusion about special cases; wenzelm parents: 66453 diff changeset	7	imports "HOL-SPARK.SPARK"
41561 d1318f3c86ba Added new SPARK verification environment. berghofe parents: diff changeset	8	begin
d1318f3c86ba Added new SPARK verification environment. berghofe parents: diff changeset	9
69605 a96320074298 isabelle update -u path_cartouches; wenzelm parents: 66992 diff changeset	10	spark_open \<open>sqrt/isqrt\<close>
41561 d1318f3c86ba Added new SPARK verification environment. berghofe parents: diff changeset	11
d1318f3c86ba Added new SPARK verification environment. berghofe parents: diff changeset	12	spark_vc function_isqrt_4
d1318f3c86ba Added new SPARK verification environment. berghofe parents: diff changeset	13	proof -
63167 0909deb8059b isabelle update_cartouches -c -t; wenzelm parents: 58130 diff changeset	14	from \<open>0 \<le> r\<close> have "(r = 0 \<or> r = 1 \<or> r = 2) \<or> 2 < r" by auto
41561 d1318f3c86ba Added new SPARK verification environment. berghofe parents: diff changeset	15	then show "2 * r \<le> 2147483646"
d1318f3c86ba Added new SPARK verification environment. berghofe parents: diff changeset	16	proof
d1318f3c86ba Added new SPARK verification environment. berghofe parents: diff changeset	17	assume "2 < r"
d1318f3c86ba Added new SPARK verification environment. berghofe parents: diff changeset	18	then have "0 < r" by simp
63167 0909deb8059b isabelle update_cartouches -c -t; wenzelm parents: 58130 diff changeset	19	with \<open>2 < r\<close> have "2 * r < r * r" by (rule mult_strict_right_mono)
0909deb8059b isabelle update_cartouches -c -t; wenzelm parents: 58130 diff changeset	20	with \<open>r * r \<le> n\<close> and \<open>n \<le> 2147483647\<close> show ?thesis
41561 d1318f3c86ba Added new SPARK verification environment. berghofe parents: diff changeset	21	by simp
d1318f3c86ba Added new SPARK verification environment. berghofe parents: diff changeset	22	qed auto
d1318f3c86ba Added new SPARK verification environment. berghofe parents: diff changeset	23	then show "2 * r \<le> 2147483647" by simp
d1318f3c86ba Added new SPARK verification environment. berghofe parents: diff changeset	24	qed
d1318f3c86ba Added new SPARK verification environment. berghofe parents: diff changeset	25
d1318f3c86ba Added new SPARK verification environment. berghofe parents: diff changeset	26	spark_end
d1318f3c86ba Added new SPARK verification environment. berghofe parents: diff changeset	27
d1318f3c86ba Added new SPARK verification environment. berghofe parents: diff changeset	28	end

author	wenzelm
	Sun, 06 Jan 2019 15:04:34 +0100
changeset 69605	a96320074298
parent 66992	69673025292e
permissions	-rw-r--r--