Theory Sqrt

(*  Title:      HOL/SPARK/Examples/Sqrt/Sqrt.thy
    Author:     Stefan Berghofer
    Copyright:  secunet Security Networks AG
*)

theory Sqrt
imports "HOL-SPARK.SPARK"
begin

spark_open ‹sqrt/isqrt›

spark_vc function_isqrt_4
proof -
  from 0  r have "(r = 0  r = 1  r = 2)  2 < r" by auto
  then show "2 * r  2147483646"
  proof
    assume "2 < r"
    then have "0 < r" by simp
    with 2 < r have "2 * r < r * r" by (rule mult_strict_right_mono)
    with r * r  n and n  2147483647 show ?thesis
      by simp
  qed auto
  then show "2 * r  2147483647" by simp
qed

spark_end

end