in mcs



--
-- ------------------- proof inv7 -------------------
--

--
-- (I) Base case
open INV .
-- fresh constants
ops p q : -> Pid .
-- check
red inv7(init,p,q) .
close


-- (II) Induction case

open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
eq (pc(s,r) = rs) = false .
-- check
red inv7(s,p,q) implies inv7(want(s,r),p,q) .
close

-- 1. want(s,r)
-- -- 1.1 pc(s,r) != rs
open INV .

op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
eq (pc(s,r) = rs) = false .
-- check
red inv7(s,p,q) implies inv7(want(s,r),p,q) .
close


-- 1.2.1 pc(s,r) = rs, p = r, q = r
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = rs .
eq p = r .
eq q = r .
-- check
red inv7(s,p,q) implies inv7(want(s,r),p,q) .
close

-- -- 1.2.2 pc(s,r) = rs, (p = r) = false, q = r
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = rs .
eq (p = r) = false .
eq q = r .
-- check
red inv7(s,p,q) implies inv7(want(s,r),p,q) .
close

-- -- 1.2.3 pc(s,r) = rs, (p = r) = false, (q = r) = false
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = rs .
eq (p = r) = false .
eq (q = r) = false .
-- check
red inv7(s,p,q) implies inv7(want(s,r),p,q) .
close

-- -- 1.2.4 pc(s,r) = rs,  p = r, (q = r) = false
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = rs .
eq (q = r) = false .
eq p = r .
-- check
red inv7(s,p,q) implies inv7(want(s,r),p,q) .
close



-- 2. stnxt(s,r)
-- -- 1.1 pc(s,r) != l1
open INV .

op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
eq (pc(s,r) = l1) = false .
-- check
red inv7(s,p,q) implies inv7(stnxt(s,r),p,q) .
close


-- 2.2.1 pc(s,r) = l1, p = r, q = r
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l1 .
eq p = r .
eq q = r .
-- check
red inv7(s,p,q) implies inv7(stnxt(s,r),p,q) .
close

-- -- 2.2.2 pc(s,r) = l1, (p = r) = false, q = r
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l1 .
eq (p = r) = false .
eq q = r .
-- check
red inv7(s,p,q) implies inv7(stnxt(s,r),p,q) .
close

-- -- 2.2.3 pc(s,r) = l1, (p = r) = false, (q = r) = false
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l1 .
eq (p = r) = false .
eq (q = r) = false .
-- check
red inv7(s,p,q) implies inv7(stnxt(s,r),p,q) .
close

-- -- 2.2.4 pc(s,r) = l1,  p = r, (q = r) = false
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l1 .
eq (q = r) = false .
eq p = r .
-- check
red inv7(s,p,q) implies inv7(stnxt(s,r),p,q) .
close



-- 3. stprd(s,r)
-- -- 3.1 pc(s,r) != l2
open INV .

op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
eq (pc(s,r) = l2) = false .
-- check
red inv7(s,p,q) implies inv7(stprd(s,r),p,q) .
close


-- 3.2.1 pc(s,r) = l2, p = r, q = r
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l2 .
eq p = r .
eq q = r .
-- check
red inv7(s,p,q) implies inv7(stprd(s,r),p,q) .
close

-- -- 3.2.2 pc(s,r) = l2, (p = r) = false, q = r
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l2 .
eq (p = r) = false .
eq q = r .
-- check
red inv7(s,p,q) implies inv7(stprd(s,r),p,q) .
close

-- -- 3.2.3 pc(s,r) = l2, (p = r) = false, (q = r) = false
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l2 .
eq (p = r) = false .
eq (q = r) = false .
-- check
red inv7(s,p,q) implies inv7(stprd(s,r),p,q) .
close

-- -- 3.2.4 pc(s,r) = l2,  p = r, (q = r) = false
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l2 .
eq (q = r) = false .
eq p = r .
-- check
red inv7(s,p,q) implies inv7(stprd(s,r),p,q) .
close


-- 4. stprd(s,r)
-- -- 4.1 pc(s,r) != l3
open INV .

op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
eq (pc(s,r) = l3) = false .
-- check
red inv7(s,p,q) implies inv7(chprd(s,r),p,q) .
close

-- 4.2.1.1 pc(s,r) = l3, p = r, q = r, pred(s,r) = nop
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l3 .
eq p = r .
eq q = r .
eq pred(s,r) = nop .
-- check
red inv7(s,p,q) implies inv7(chprd(s,r),p,q) .
close

-- 4.2.1.2 pc(s,r) = l3, p = r, q = r, pred(s,r) != nop
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l3 .
eq p = r .
eq q = r .

eq (pred(s,r) = nop) = false .
-- check
red inv7(s,p,q) implies inv7(chprd(s,r),p,q) .
close

-- -- 4.2.2.1 pc(s,r) = l3, (p = r) = false, q = r,pred(s,r) != nop
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l3 .
eq (p = r) = false .
eq q = r .

eq (pred(s,r) = nop) = false .
-- check
red inv7(s,p,q) implies inv7(chprd(s,r),p,q) .
close

-- -- 4.2.2.2 pc(s,r) = l3, (p = r) = false, q = r,pred(s,r) = nop
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l3 .
eq (p = r) = false .
eq q = r .

eq pred(s,r) = nop .
-- check
red inv7(s,p,q) implies inv7(chprd(s,r),p,q) .
close


-- -- 4.2.3 pc(s,r) = l3, (p = r) = false, (q = r) = false
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l3 .
eq (p = r) = false .
eq (q = r) = false .
-- check
red inv7(s,p,q) implies inv7(chprd(s,r),p,q) .
close

-- -- 4.2.4.1 pc(s,r) = l3,  p = r, (q = r) = false, pred(s,r) != nop .
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l3 .
eq (q = r) = false .
eq p = r .
eq (pred(s,r) = nop) = false .
-- check
red inv7(s,p,q) implies inv7(chprd(s,r),p,q) .
close

-- -- 4.2.4.2 pc(s,r) = l3,  p = r, (q = r) = false, pred(s,r) = nop .
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l3 .
eq (q = r) = false .
eq p = r .
eq pred(s,r) = nop .

-- check
red  ( inv7(s,p,q)) implies inv7(chprd(s,r),p,q) .
close


-- 5. stlck(s,r)
-- -- 5.1 pc(s,r) != l4
open INV .

op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
eq (pc(s,r) = l4) = false .
-- check
red inv7(s,p,q) implies inv7(stlck(s,r),p,q) .
close


-- 5.2.1 pc(s,r) = l4, p = r, q = r
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l4 .
eq p = r .
eq q = r .
-- check
red inv7(s,p,q) implies inv7(stlck(s,r),p,q) .
close

-- -- 5.2.2 pc(s,r) = l4, (p = r) = false, q = r
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l4 .
eq (p = r) = false .
eq q = r .
-- check
red inv7(s,p,q) implies inv7(stlck(s,r),p,q) .
close

-- -- 5.2.3 pc(s,r) = l4, (p = r) = false, (q = r) = false
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l4 .
eq (p = r) = false .
eq (q = r) = false .
-- check
red inv7(s,p,q) implies inv7(stlck(s,r),p,q) .
close

-- -- 5.2.4 pc(s,r) = l4,  p = r, (q = r) = false
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l4 .
eq (q = r) = false .
eq p = r .
-- check
red inv7(s,p,q) implies inv7(stlck(s,r),p,q) .
close


-- 6. stnpr(s,r)
-- -- 6.1 pc(s,r) != l5
open INV .

op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
eq (pc(s,r) = l5) = false .
-- check
red inv7(s,p,q) implies inv7(stnpr(s,r),p,q) .
close


-- 6.2.1 pc(s,r) = l5, p = r, q = r
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l5 .
eq p = r .
eq q = r .

-- eq lock(s,r) = true .
-- check
red (inv7(s,p,q) and lemma21(s,r)) implies inv7(stnpr(s,r),p,q) .
close

-- -- 6.2.2.1 pc(s,r) = l5, (p = r) = false, q = r, lock(s,r) = true .
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l5 .
eq (p = r) = false .
eq q = r .
eq lock(s,r) = true .
-- check
red inv7(s,p,q) implies inv7(stnpr(s,r),p,q) .
close


-- -- 6.2.2.2 pc(s,r) = l5, (p = r) = false, q = r, lock(s,r) = false .
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l5 .
eq (p = r) = false .
eq q = r .
eq lock(s,r) = false .

-- check
red (inv6(s,r) and inv7(s,p,q)) implies inv7(stnpr(s,r),p,q) .
close


-- -- 6.2.3 pc(s,r) = l5, (p = r) = false, (q = r) = false
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l5 .
eq (p = r) = false .
eq (q = r) = false .
-- check
red inv7(s,p,q) implies inv7(stnpr(s,r),p,q) .
close


-- -- 6.2.4.1 pc(s,r) = l5,  p = r, (q = r) = false, lock(s,r) = true
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l5 .
eq (q = r) = false .
eq p = r .
eq lock(s,r) = true .
-- check
red inv7(s,p,q) implies inv7(stnpr(s,r),p,q) .
close

-- -- 6.2.4.2 pc(s,r) = l5,  p = r, (q = r) = false, lock(s,r) = false
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l5 .
eq (q = r) = false .
eq p = r .
eq lock(s,r) = false .
-- check
red (inv6(s,r) and inv7(s,p,q)) implies inv7(stnpr(s,r),p,q) .
close

-- 7. chlck(s,r)
-- -- 7.1 pc(s,r) != l6
open INV .

op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
eq (pc(s,r) = l6) = false .
-- check
red inv7(s,p,q) implies inv7(chlck(s,r),p,q) .
close

-- 7.2.1 pc(s,r) = l6, p = r, q = r
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l6 .
eq p = r .
eq q = r .

-- check
red inv7(s,p,q) implies inv7(chlck(s,r),p,q) .
close

-- -- 7.2.2 pc(s,r) = l6, (p = r) = false, q = r
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l6 .
eq (p = r) = false .
eq q = r .

-- check
red inv7(s,p,q) implies inv7(chlck(s,r),p,q) .
close



-- -- 7.2.3 pc(s,r) = l6, (p = r) = false, (q = r) = false
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l6 .
eq (p = r) = false .
eq (q = r) = false .

-- check
red inv7(s,p,q) implies inv7(chlck(s,r),p,q) .
close


-- -- 7.2.4 pc(s,r) = l6,  p = r, (q = r) = false
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l6 .
eq (q = r) = false .
eq p = r .

-- check
red inv7(s,p,q) implies inv7(chlck(s,r),p,q) .
close

-- 8. exit(s,r)
-- -- 8.1 pc(s,r) != cs
open INV .

op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
eq (pc(s,r) = cs) = false .
-- check
red inv7(s,p,q) implies inv7(exit(s,r),p,q) .
close


-- 8.2.1 pc(s,r) = cs, p = r, q = r
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = cs .
eq p = r .
eq q = r .
-- check
red inv7(s,p,q) implies inv7(exit(s,r),p,q) .
close

-- -- 8.2.2 pc(s,r) = cs, (p = r) = false, q = r
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = cs .
eq (p = r) = false .
eq q = r .

-- check
red  (mutex(s,p,r) and inv7(s,p,q)) implies inv7(exit(s,r),p,q) .
close

-- -- 8.2.3 pc(s,r) = cs, (p = r) = false, (q = r) = false
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = cs .
eq (p = r) = false .
eq (q = r) = false .
-- check
red inv7(s,p,q) implies inv7(exit(s,r),p,q) .
close

-- -- 8.2.4 pc(s,r) = cs,  p = r, (q = r) = false
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = cs .
eq (q = r) = false .
eq p = r .
-- check
red inv7(s,p,q) implies inv7(exit(s,r),p,q) .
close


-- 9. chnxt(s,r)
-- -- 9.1 pc(s,r) != l7
open INV .
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
eq (pc(s,r) = l7) = false .
-- check
red inv7(s,p,q) implies inv7(chnxt(s,r),p,q) .
close


-- 9.2.1.1 pc(s,r) = l7, p = r, q = r, next(s,r) = nop
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l7 .
eq p = r .
eq q = r .

eq next(s,r) = nop .
-- check
red inv7(s,p,q) implies inv7(chnxt(s,r),p,q) .
close


-- 9.2.1.2 pc(s,r) = l7, p = r, q = r, next(s,r) != nop
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l7 .
eq p = r .
eq q = r .

eq (next(s,r) = nop) = false  .
-- check
red inv7(s,p,q) implies inv7(chnxt(s,r),p,q) .
close

-- -- 9.2.2.1 pc(s,r) = l7, (p = r) = false, q = r, next(s,r) = nop
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l7 .
eq (p = r) = false .
eq q = r .
eq next(s,r) = nop .
-- check

red inv7(s,p,q) implies inv7(chnxt(s,r),p,q) .
close

-- -- 9.2.2.1 pc(s,r) = l7, (p = r) = false, q = r, next(s,r) != nop
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l7 .
eq (p = r) = false .
eq q = r .
eq (next(s,r) = nop) = false .
-- check

red inv7(s,p,q) implies inv7(chnxt(s,r),p,q) .
close

-- -- 9.2.3 pc(s,r) = l7, (p = r) = false, (q = r) = false
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l7 .
eq (p = r) = false .
eq (q = r) = false .
-- check
red inv7(s,p,q) implies inv7(chnxt(s,r),p,q) .
close

-- -- 9.2.4.1 pc(s,r) = l7,  p = r, (q = r) = false, next(s,r) != nop
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l7 .
eq (q = r) = false .
eq p = r .
eq (next(s,r) = nop) = false  .
-- check
red inv7(s,p,q) implies inv7(chnxt(s,r),p,q) .
close

-- -- 9.2.4.2 pc(s,r) = l7,  p = r, (q = r) = false, next(s,r) = nop
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l7 .
eq (q = r) = false .
eq p = r .
eq next(s,r) = nop  .
-- check
red inv7(s,p,q) implies inv7(chnxt(s,r),p,q) .
close

-- 10. chglk(s,r)
-- -- 10.1 pc(s,r) != l8
open INV .

op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
eq (pc(s,r) = l8) = false .
-- check
red inv7(s,p,q) implies inv7(chglk(s,r),p,q) .
close


-- 10.2.1.1 pc(s,r) = l8, p = r, q = r, r = glock(s)
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l8 .
eq p = r .
eq q = r .
eq glock(s) = r .

-- check
red inv7(s,p,q) implies inv7(chglk(s,r),p,q) .
close


-- 10.2.1.2 pc(s,r) = l8, p = r, q = r, r != glock(s)
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l8 .
eq p = r .
eq q = r .
eq (glock(s) = r) = false .

-- check
red inv7(s,p,q) implies inv7(chglk(s,r),p,q) .
close


-- -- 10.2.2.1 pc(s,r) = l8, (p = r) = false, q = r
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l8 .
eq (p = r) = false .
eq q = r .
eq glock(s) = r .
-- check
red inv7(s,p,q) implies inv7(chglk(s,r),p,q) .
close

-- -- 10.2.2.2 pc(s,r) = l8, (p = r) = false, q = r, glock != r
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l8 .
eq (p = r) = false .
eq q = r .
eq (glock(s) = r) = false .
-- check
red inv7(s,p,q) implies inv7(chglk(s,r),p,q) .
close

-- -- 10.2.3 pc(s,r) = l8, (p = r) = false, (q = r) = false
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l8 .
eq (p = r) = false .
eq (q = r) = false .
-- check
red inv7(s,p,q) implies inv7(chglk(s,r),p,q) .
close

-- 10.2.4.1 pc(s,r) = l8,  p = r, (q = r) = false, (glock(s) = r) = false .
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l8 .
eq (q = r) = false .
eq p = r .

eq (glock(s) = r) = false .
-- check
red inv7(s,p,q) implies inv7(chglk(s,r),p,q) .
close

-- -- 10.2.4.2 pc(s,r) = l8,  p = r, (q = r) = false, (glock(s) = r) .
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l8 .
eq (q = r) = false .
eq p = r .

eq glock(s) = r .
-- check
red inv7(s,p,q) implies inv7(chglk(s,r),p,q) .
close


-- 11. go2rs(s,r)
-- -- 11.1 pc(s,r) != l9
open INV .

op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
eq (pc(s,r) = l9) = false .
-- check
red inv7(s,p,q) implies inv7(go2rs(s,r),p,q) .
close


-- 11.2.1 pc(s,r) = l9, p = r, q = r
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l9 .
eq p = r .
eq q = r .
-- check
red inv7(s,p,q) implies inv7(go2rs(s,r),p,q) .
close

-- -- 11.2.2 pc(s,r) = l9, (p = r) = false, q = r
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l9 .
eq (p = r) = false .
eq q = r .
-- check
red inv7(s,p,q) implies inv7(go2rs(s,r),p,q) .
close

-- -- 11.2.3 pc(s,r) = l9, (p = r) = false, (q = r) = false
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l9 .
eq (p = r) = false .
eq (q = r) = false .
-- check
red inv7(s,p,q) implies inv7(go2rs(s,r),p,q) .
close

-- -- 11.2.4 pc(s,r) = l9,  p = r, (q = r) = false
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l9 .
eq (q = r) = false .
eq p = r .
-- check
red inv7(s,p,q) implies inv7(go2rs(s,r),p,q) .
close

-- 12. chnxt2(s,r)
-- -- 10.1 pc(s,r) != l10
open INV .

op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
eq (pc(s,r) = l10) = false .
-- check
red inv7(s,p,q) implies inv7(chnxt2(s,r),p,q) .
close


-- 12.2.1.1 pc(s,r) = l10, p = r, q = r, next(s,r) = nop
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l10 .
eq p = r .
eq q = r .

eq next(s,r) = nop .
-- check
red inv7(s,p,q) implies inv7(chnxt2(s,r),p,q) .
close

-- 12.2.1.2 pc(s,r) = l10, p = r, q = r, next(s,r) != nop
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l10 .
eq p = r .
eq q = r .

eq (next(s,r) = nop) = false .
-- check
red inv7(s,p,q) implies inv7(chnxt2(s,r),p,q) .
close

-- -- 12.2.2.1 pc(s,r) = l10, (p = r) = false, q = r, next(s,r) = nop
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l10 .
eq (p = r) = false .
eq q = r .
eq next(s,r) = nop .
-- check
red inv7(s,p,q) implies inv7(chnxt2(s,r),p,q) .
close

-- -- 12.2.2.2 pc(s,r) = l10, (p = r) = false, q = r, next(s,r) != nop
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l10 .
eq (p = r) = false .
eq q = r .
eq (next(s,r) = nop) = false .
-- check
red inv7(s,p,q) implies inv7(chnxt2(s,r),p,q) .
close


-- -- 12.2.3 pc(s,r) = l10, (p = r) = false, (q = r) = false
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l10 .
eq (p = r) = false .
eq (q = r) = false .
-- check
red inv7(s,p,q) implies inv7(chnxt2(s,r),p,q) .
close


-- -- 12.2.4.1 pc(s,r) = l10,  p = r, (q = r) = false, (next(s,r) = nop) = false .
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l10 .
eq (q = r) = false .
eq p = r .

eq (next(s,r) = nop) = false .

-- check
red inv7(s,p,q) implies inv7(chnxt2(s,r),p,q) .
close

-- -- 12.2.4.2 pc(s,r) = l10,  p = r, (q = r) = false, next(s,r) = nop .
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l10 .
eq (q = r) = false .
eq p = r .

eq next(s,r) = nop .
-- check
red inv7(s,p,q) implies inv7(chnxt2(s,r),p,q) .
close

-- 13. stlnx(s,r)
-- -- 13.1 pc(s,r) != l11
open INV .
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
eq (pc(s,r) = l11) = false .
-- check
red inv7(s,p,q) implies inv7(stlnx(s,r),p,q) .
close


-- 13.2.1 pc(s,r) = l11, p = r, q = r
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l11 .
eq p = r .
eq q = r .
-- check
red inv7(s,p,q) implies inv7(stlnx(s,r),p,q) .
close

-- -- 13.2.2 pc(s,r) = l11, (p = r) = false, q = r
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l11 .
eq (p = r) = false .
eq q = r .
-- check
red inv7(s,p,q) implies inv7(stlnx(s,r),p,q) .
close


-- -- 13.2.3.1a pc(s,r) = l11, (p = r) = false, (q = r) = false, q != p,  next(s,r) = q
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l11 .
eq (p = r) = false .
eq (q = r) = false .

eq (q = p) = false .
eq next(s,r) = q .
-- check

red (lemma32(s,r,p) and inv7(s,p,q) ) implies inv7(stlnx(s,r),p,q) .
close

-- -- 13.2.3.1b.1 pc(s,r) = l11, (p = r) = false, (q = r) = false, q != p,  next(s,r) != q, lock(s,q) = false .
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l11 .
eq (p = r) = false .
eq (q = r) = false .

eq (q = p) = false .
eq (next(s,r) = q) = false .
eq lock(s,q) = false .

-- check
red ( lemma32(s,r,q) and inv7(s,p,q) ) implies inv7(stlnx(s,r),p,q) .
close

-- -- 13.2.3.1b.2 pc(s,r) = l11, (p = r) = false, (q = r) = false, q != p,  next(s,r) != q, lock(s,q) = true .
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l11 .
eq (p = r) = false .
eq (q = r) = false .

eq (q = p) = false .
eq (next(s,r) = q) = false .
eq lock(s,q) = true .

-- check
red ( lemma32(s,r,q) and inv7(s,p,q) ) implies inv7(stlnx(s,r),p,q) .
close


-- -- 13.2.3.2 pc(s,r) = l11, (p = r) = false, (q = r) = false, q = p,
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l11 .
eq (p = r) = false .
eq (q = r) = false .

eq q = p .
-- check
red (  inv7(s,p,q) ) implies inv7(stlnx(s,r),p,q) .
close


-- -- 13.2.4 pc(s,r) = l11,  p = r, (q = r) = false
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l11 .
eq (q = r) = false .
eq p = r .
-- check
red inv7(s,p,q) implies inv7(stlnx(s,r),p,q) .
close


-- 14. go2rs2(s,r)
-- -- 14.1 pc(s,r) != l12
open INV .
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
eq (pc(s,r) = l12) = false .
-- check
red inv7(s,p,q) implies inv7(go2rs2(s,r),p,q) .
close


-- 14.2.1 pc(s,r) = l12, p = r, q = r
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l12 .
eq p = r .
eq q = r .
-- check
red inv7(s,p,q) implies inv7(go2rs2(s,r),p,q) .
close

-- -- 14.2.2 pc(s,r) = l11, (p = r) = false, q = r
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l12 .
eq (p = r) = false .
eq q = r .
-- check
red inv7(s,p,q) implies inv7(go2rs2(s,r),p,q) .
close



-- -- 14.2.3 pc(s,r) = l11, (p = r) = false, (q = r) = false
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l12 .
eq (p = r) = false .
eq (q = r) = false .
-- check
red inv7(s,p,q) implies inv7(go2rs2(s,r),p,q) .
close

-- -- 14.2.4 pc(s,r) = l11,  p = r, (q = r) = false
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] : inv7(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l12 .
eq (q = r) = false .
eq p = r .
-- check
red inv7(s,p,q) implies inv7(go2rs2(s,r),p,q) .
close


eof .