--> ****************************************************************
-->           PROOF score for the initial states condition 
--> ****************************************************************

--> ----------------------------------------------------------------
--> require qlock-prop
require qlock-prop

--> ----------------------------------------------------------------
--> INITcheck: module for checking initial condition 
--> ----------------------------------------------------------------
mod INITcheck {
inc(INIT + MX + HQ=C)
pred check-init_ : State .
eq (check-init S:State) = (init S) implies ((mx S) and (hq=c S)) .
-- fresh constants
op aq : -> Aq .
ops as-r as-w as-c : -> As .
-- initial condition proposition
op initCheck : -> Bool .
eq initCheck = check-init [aq r as-r w as-w c as-c] .
}

--> ================================================================
--> check that (init implies q=wc)
--> ----------------------------------------------------------------
select INITcheck .
:goal{eq initCheck = true .}
:def csp-q = :csp{eq aq = empQ . eq (aq =aq empQ) = false .}
:def csp-r = :csp{eq as-r = empS . eq (as-r =as empS) = false .}
:def csp-w = :csp{eq as-w = empS . eq (as-w =as empS) = false .}
:def csp-c = :csp{eq as-c = empS . eq (as-c =as empS) = false .}
:apply(csp-q rd- csp-r rd- csp-w rd- csp-c rd-) 
--> QED
--> ================================================================

--> ****************************************************************
--> end of file
eof
--> ****************************************************************