isabelle: src/HOL/SPARK/Examples/Sqrt/Sqrt.thy@e3e7c86168b4 (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
d1318f3c86ba Added new SPARK verification environment. berghofe parents: diff changeset	7	imports SPARK
d1318f3c86ba Added new SPARK verification environment. berghofe parents: diff changeset	8	begin
d1318f3c86ba Added new SPARK verification environment. berghofe parents: diff changeset	9
56798 939e88e79724 Discontinued old spark_open; spark_open_siv is now spark_open berghofe parents: 41561 diff changeset	10	spark_open "sqrt/isqrt"
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 -
d1318f3c86ba Added new SPARK verification environment. berghofe parents: diff changeset	14	from `0 \<le> r` have "(r = 0 \<or> r = 1 \<or> r = 2) \<or> 2 < r" by auto
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
d1318f3c86ba Added new SPARK verification environment. berghofe parents: diff changeset	19	with `2 < r` have "2 * r < r * r" by (rule mult_strict_right_mono)
d1318f3c86ba Added new SPARK verification environment. berghofe parents: diff changeset	20	with `r * r \<le> n` and `n \<le> 2147483647` show ?thesis
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	desharna
	Wed, 16 Jul 2014 10:13:00 +0200
changeset 57563	e3e7c86168b4
parent 56798	939e88e79724
child 58130	5e9170812356
permissions	-rw-r--r--