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(* Title: OAWN_SOS_Labels.thy
License: BSD 2-Clause. See LICENSE.
Author: Timothy Bourke
*)
section "Configure the inv-cterms tactic for open sequential processes"
theory OAWN_SOS_Labels
imports OAWN_SOS Inv_Cterms
begin
lemma oelimder_guard:
assumes "p = {l}\<langle>fg\<rangle> qq"
and "l' \<in> labels \<Gamma> q"
and "((\<sigma>, p), a, (\<sigma>', q)) \<in> oseqp_sos \<Gamma> i"
obtains p' where "p = {l}\<langle>fg\<rangle> p'"
and "l' \<in> labels \<Gamma> qq"
using assms by auto
lemma oelimder_assign:
assumes "p = {l}\<lbrakk>fa\<rbrakk> qq"
and "l' \<in> labels \<Gamma> q"
and "((\<sigma>, p), a, (\<sigma>', q)) \<in> oseqp_sos \<Gamma> i"
obtains p' where "p = {l}\<lbrakk>fa\<rbrakk> p'"
and "l' \<in> labels \<Gamma> qq"
using assms by auto
lemma oelimder_ucast:
assumes "p = {l}unicast(fip, fmsg).q1 \<triangleright> q2"
and "l' \<in> labels \<Gamma> q"
and "((\<sigma>, p), a, (\<sigma>', q)) \<in> oseqp_sos \<Gamma> i"
obtains p' pp' where "p = {l}unicast(fip, fmsg).p' \<triangleright> pp'"
and "case a of unicast _ _ \<Rightarrow> l' \<in> labels \<Gamma> q1
| _ \<Rightarrow> l' \<in> labels \<Gamma> q2"
using assms by simp (erule oseqpTEs, auto)
lemma oelimder_bcast:
assumes "p = {l}broadcast(fmsg).qq"
and "l' \<in> labels \<Gamma> q"
and "((\<sigma>, p), a, (\<sigma>', q)) \<in> oseqp_sos \<Gamma> i"
obtains p' where "p = {l}broadcast(fmsg). p'"
and "l' \<in> labels \<Gamma> qq"
using assms by auto
lemma oelimder_gcast:
assumes "p = {l}groupcast(fips, fmsg).qq"
and "l' \<in> labels \<Gamma> q"
and "((\<sigma>, p), a, (\<sigma>', q)) \<in> oseqp_sos \<Gamma> i"
obtains p' where "p = {l}groupcast(fips, fmsg). p'"
and "l' \<in> labels \<Gamma> qq"
using assms by auto
lemma oelimder_send:
assumes "p = {l}send(fmsg).qq"
and "l' \<in> labels \<Gamma> q"
and "((\<sigma>, p), a, (\<sigma>', q)) \<in> oseqp_sos \<Gamma> i"
obtains p' where "p = {l}send(fmsg). p'"
and "l' \<in> labels \<Gamma> qq"
using assms by auto
lemma oelimder_deliver:
assumes "p = {l}deliver(fdata).qq"
and "l' \<in> labels \<Gamma> q"
and "((\<sigma>, p), a, (\<sigma>', q)) \<in> oseqp_sos \<Gamma> i"
obtains p' where "p = {l}deliver(fdata).p'"
and "l' \<in> labels \<Gamma> qq"
using assms by auto
lemma oelimder_receive:
assumes "p = {l}receive(fmsg).qq"
and "l' \<in> labels \<Gamma> q"
and "((\<sigma>, p), a, (\<sigma>', q)) \<in> oseqp_sos \<Gamma> i"
obtains p' where "p = {l}receive(fmsg).p'"
and "l' \<in> labels \<Gamma> qq"
using assms by auto
lemmas oelimders =
oelimder_guard
oelimder_assign
oelimder_ucast
oelimder_bcast
oelimder_gcast
oelimder_send
oelimder_deliver
oelimder_receive
declare
oseqpTEs [cterms_seqte]
oelimders [cterms_elimders]
end
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