lh-l4v/proof/sep-capDL/Sep_Tactic_Helper.thy

(*
 * Copyright 2014, NICTA
 *
 * This software may be distributed and modified according to the terms of
 * the GNU General Public License version 2. Note that NO WARRANTY is provided.
 * See "LICENSE_GPLv2.txt" for details.
 *
 * @TAG(NICTA_GPL)
 *)

theory Sep_Tactic_Helper
imports
  "../../lib/Hoare_Sep_Tactics/Hoare_Sep_Tactics"
  "../../lib/sep_algebra/MonadSep"
begin

lemma no_exception_conjE:
  "\<lbrakk>\<lbrace>P'\<rbrace> f \<lbrace>Q\<rbrace>, -; \<lbrace>P\<rbrace> f \<lbrace>Q'\<rbrace>, \<lbrace>E\<rbrace>\<rbrakk> \<Longrightarrow> \<lbrace>P and P'\<rbrace> f \<lbrace>\<lambda>r s. Q r s \<and> Q' r s\<rbrace>, \<lbrace>E\<rbrace>"
  by (fastforce simp: validE_def validE_R_def valid_def split: sum.splits)

definition
  sep_any :: "('b \<Rightarrow> 'c \<Rightarrow> ('a \<Rightarrow> bool)) \<Rightarrow> ('b \<Rightarrow> ('a \<Rightarrow> bool))" where
  "sep_any m \<equiv> (\<lambda>p s. \<exists>v. (m p v) s)"

lemma sep_any_imp[sep_cancel]: "(m p e) s \<Longrightarrow> sep_any m p s"
  by (fastforce simp: sep_any_def)

end