Theory S_L

(*  Title:      HOL/SPARK/Examples/RIPEMD-160/S_L.thy
    Author:     Fabian Immler, TU Muenchen

Verification of the RIPEMD-160 hash function
*)

theory S_L
imports RMD_Specification RMD_Lemmas
begin

spark_open "rmd/s_l"

spark_vc function_s_l_2
proof -
  from `0 ≤ j` `j ≤ 79`
  show C: ?C1
    by (simp add: s_def s_list_def nth_map [symmetric, of _ _ int] del: fun_upd_apply)
      (simp add: nth_fun_of_list_eq [of _ _ undefined] del: fun_upd_apply)
  from C show ?C2 by simp
  have "list_all (λn. int n ≤ 15) s_list"
    by (simp add: s_list_def)
  moreover have "length s_list = 80"
    by (simp add: s_list_def)
  ultimately show ?C3 unfolding C using `j ≤ 79`
    by (simp add: s_def list_all_length)
qed

spark_end

end