(* Title: HOL/SPARK/Examples/RIPEMD-160/S_R.thy
Author: Fabian Immler, TU Muenchen
Verification of the RIPEMD-160 hash function
*)
theory S_R
imports RMD_Specification RMD_Lemmas
begin
spark_open \<open>rmd/s_r\<close>
spark_vc function_s_r_2
proof -
from \<open>0 \<le> j\<close> \<open>j \<le> 79\<close>
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 (\<lambda>n. int n \<le> 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 \<open>j \<le> 79\<close>
by (simp add: s'_def list_all_length)
qed
spark_end
end