Theory Simple_Greatest_Common_Divisor

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

theory Simple_Greatest_Common_Divisor
imports "HOL-SPARK.SPARK"
begin

spark_proof_functions
  gcd = "gcd :: int ⇒ int ⇒ int"

spark_open ‹simple_greatest_common_divisor/g_c_d›

spark_vc procedure_g_c_d_4
  using ‹0 < d› ‹gcd c d = gcd m n›
  by (simp add: gcd_non_0_int)

spark_vc procedure_g_c_d_9
  using ‹0 ≤ c› ‹gcd c 0 = gcd m n›
  by simp

spark_end

end