in mcs


--
-- ------------------- proof lemma 1_2 -------------------
--

--
-- (I) Base case
open INV .
-- fresh constants
ops p q : -> Pid .
-- check
red   inv10(init,p,q) .
close


-- (II) Induction case

-- 1. want(s,r)
-- 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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = rs .
eq p = r .
eq q = r .
-- check
red   inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = rs .
eq (p = r) = false .
eq q = r .
-- check
red   inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = rs .
eq (p = r) = false .
eq (q = r) = false .
-- check
red   inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = rs .
eq (q = r) = false .
eq p = r .
-- check
red   inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
eq (pc(s,r) = l1) = false .
-- check
red   inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l1 .
eq p = r .
eq q = r .
-- check
red   inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l1 .
eq (p = r) = false .
eq q = r .

-- check
red   inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l1 .
eq (p = r) = false .
eq (q = r) = false .
-- check
red   inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l1 .
eq (q = r) = false .
eq p = r .
-- check
red   inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
eq (pc(s,r) = l2) = false .
-- check
red   inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l2 .
eq p = r .
eq q = r .

-- check
red   inv10(s,p,q) implies inv10(stprd(s,r),p,q).
close

-- -- 3.2.2.1 pc(s,r) = l2, (p = r) = false, q = r, next(s,r) = p .
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l2 .
eq (p = r) = false .
eq q = r .

eq next(s,r) = p .
-- check
red   (inv10(s,p,q)) implies  inv10(stprd(s,r),p,q) .
close


-- -- 3.2.2.2 pc(s,r) = l2, (p = r) = false, q = r, next(s,r) != p .
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l2 .
eq (p = r) = false .
eq q = r .

eq (next(s,r) = p) = false .
-- check
red ( inv10(s,p,q)) implies  inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l2 .
eq (p = r) = false .
eq (q = r) = false .
-- check
red   inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l2 .
eq (q = r) = false .
eq p = r .
-- check
red   ( inv10(s,p,q)) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
eq (pc(s,r) = l3) = false .
-- check
red   inv10(s,p,q) implies   inv10(chprd(s,r),p,q) .
close

-- 4.2.1a pc(s,r) = l3, p = r, q = r
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] :   inv10(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   inv10(s,p,q) implies   inv10(chprd(s,r),p,q) .
close

-- 4.2.1b pc(s,r) = l3, p = r, q = r
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] :   inv10(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   inv10(s,p,q) implies   inv10(chprd(s,r),p,q) .
close


-- -- 4.2.2.1 pc(s,r) = l3, (p = r) = false, q = r, pc(s,p) != l5
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l3 .
eq (p = r) = false .
eq q = r .

eq (pc(s,p) = l5) = false .
-- check
red  ( inv10(s,p,q)) implies   inv10(chprd(s,r),p,q) .
close

-- -- 4.2.2.2a pc(s,r) = l3, (p = r) = false, q = r, pc(s,p) = l5, pred(s,r) != nop
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l3 .
eq (p = r) = false .
eq q = r .

eq pc(s,p) = l5 .
eq (pred(s,r) = nop) = false .
-- check
red  ( inv10(s,p,q)) implies   inv10(chprd(s,r),p,q) .
close

-- -- 4.2.2.2b pc(s,r) = l3, (p = r) = false, q = r, pc(s,p) = l5, pred(s,r) = nop
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l3 .
eq (p = r) = false .
eq q = r .

eq pc(s,p) = l5 .
eq pred(s,r) = nop .
-- check
red  ( inv10(s,p,q)) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l3 .
eq (p = r) = false .
eq (q = r) = false .
-- check
red   inv10(s,p,q) implies   inv10(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] :   inv10(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  ( inv10(s,p,q)) implies   inv10(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] :   inv10(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  ( inv10(s,p,q)) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
eq (pc(s,r) = l4) = false .
-- check
red   inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l4 .
eq p = r .
eq q = r .
-- check
red   inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l4 .
eq (p = r) = false .
eq q = r .
-- check
red   inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l4 .
eq (p = r) = false .
eq (q = r) = false .
-- check
red   inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l4 .
eq (q = r) = false .
eq p = r .
-- check
red  ( inv10(s,p,q)) implies inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
eq (pc(s,r) = l5) = false .
-- check
red   inv10(s,p,q) implies   inv10(stnpr(s,r),p,q) .
close


-- 6.2.1 pc(s,r) = l5, p = r, q = r, lock(s,r) = true
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l5 .
eq p = r .
eq q = r .

eq pred(s,r) = r .
-- check
red   (inv14(s,r) and inv10(s,p,q)) implies   inv10(stnpr(s,r),p,q) .
close

-- 6.2.1 pc(s,r) = l5, p = r, q = r, lock(s,r) = true
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l5 .
eq p = r .
eq q = r .
eq lock(s,r) = true .
eq (pred(s,r) = r) = false .
-- check
eq lock(s,r) = true . red   (inv10(s,p,q)) implies   inv10(stnpr(s,r),p,q) .
eq lock(s,r) = false . red   (inv10(s,p,q)) implies   inv10(stnpr(s,r),p,q) .
close

-- -- 6.2.2. pc(s,r) = l5, (p = r) = false, q = r,
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l5 .
eq (p = r) = false .
eq q = r .

eq pred(s,r) = r .
-- check
red   (inv14(s,r) and inv10(s,p,q)) implies  inv10(stnpr(s,r),p,q) .
close

-- -- 6.2.2. pc(s,r) = l5, (p = r) = false, q = r,
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l5 .
eq (p = r) = false .
eq q = r .

eq (pred(s,r) = r) = false .
-- check
red   (inv10(s,p,q)) implies  inv10(stnpr(s,r),p,q) .
close

-- -- 6.2.3.1 pc(s,r) = l5, (p = r) = false, (q = r) = false, pred(s,r) = q
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l5 .
eq (p = r) = false .
eq (q = r) = false .
eq pred(s,r) = q .
-- check
red   inv10(s,p,q) implies inv10(stnpr(s,r),p,q) .
close

-- -- 6.2.3.2 pc(s,r) = l5, (p = r) = false, (q = r) = false, pred(s,r) != q
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l5 .
eq (p = r) = false .
eq (q = r) = false .
eq (pred(s,r) = q) = false .
-- check
red   inv10(s,p,q) implies inv10(stnpr(s,r),p,q) .
close


-- -- 6.2.4.1 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] :   inv10(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 inv10(s,p,q)) implies inv10(stnpr(s,r),p,q) .
close

-- -- 6.2.4.2 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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l5 .
eq (q = r) = false .
eq p = r .

eq lock(s,r) = true .
eq pred(s,r) = q .
-- check
red   (inv10(s,p,q)) implies inv10(stnpr(s,r),p,q) .
close

-- -- 6.2.4.2 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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l5 .
eq (q = r) = false .
eq p = r .

eq lock(s,r) = true .
eq (pred(s,r) = q) = false .
-- check
red   (inv10(s,p,q)) implies inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
eq (pc(s,r) = l6) = false .
-- check
red   inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l6 .
eq p = r .
eq q = r .

eq lock(s,r) = false . red  inv10(s,p,q) implies   inv10(chlck(s,r),p,q) .
eq lock(s,r) = true . red  inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l6 .
eq (p = r) = false .
eq q = r .
eq lock(s,r) = false . red  inv10(s,p,q) implies   inv10(chlck(s,r),p,q) .
eq lock(s,r) = true . red  inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l6 .
eq (p = r) = false .
eq (q = r) = false .
-- check
red   inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l6 .
eq (q = r) = false .
eq p = r .
eq lock(s,r) = false . red  inv10(s,p,q) implies   inv10(chlck(s,r),p,q) .
eq lock(s,r) = true . red  inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
eq (pc(s,r) = cs) = false .
-- check
red   inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = cs .
eq p = r .
eq q = r .
-- check
red   inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = cs .
eq (p = r) = false .
eq q = r .
-- check
red  ( inv10(s,p,q)) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = cs .
eq (p = r) = false .
eq (q = r) = false .
-- check
red   inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = cs .
eq (q = r) = false .
eq p = r .
-- check
red   inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
eq (pc(s,r) = l7) = false .
-- check
red   inv10(s,p,q) implies   inv10(chnxt(s,r),p,q) .
close

-- 9.2.1 pc(s,r) = l7, p = r, q = r
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l7 .
eq p = r .
eq q = r .
-- check
red   inv10(s,p,q) implies   inv10(chnxt(s,r),p,q) .
close

-- -- 9.2.2 pc(s,r) = l7, (p = r) = false, q = r
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l7 .
eq (p = r) = false .
eq q = r .
-- check
red   (inv10(s,p,q)) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l7 .
eq (p = r) = false .
eq (q = r) = false .
-- check
red   inv10(s,p,q) implies   inv10(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] :   inv10(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   inv10(s,p,q) implies   inv10(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] :   inv10(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   inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
eq (pc(s,r) = l8) = false .
-- check
red   inv10(s,p,q) implies   inv10(chglk(s,r),p,q) .
close

-- 10.2.1 pc(s,r) = l8, p = r, q = r
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l8 .
eq p = r .
eq q = r .
-- check
red   inv10(s,p,q) implies   inv10(chglk(s,r),p,q) .
close

-- -- 10.2.2.1 pc(s,r) = l8, (p = r) = false, q = r glock(s) = r
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] :   inv10(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   inv10(s,p,q) implies   inv10(chglk(s,r),p,q) .
close

-- -- 10.2.2.2 pc(s,r) = l8, (p = r) = false, q = r, glock(s) != r
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] :   inv10(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   ( inv10(s,p,q)) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l8 .
eq (p = r) = false .
eq (q = r) = false .
-- check
red   inv10(s,p,q) implies   inv10(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] :   inv10(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   inv10(s,p,q) implies   inv10(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] :   inv10(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   inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
eq (pc(s,r) = l9) = false .
-- check
red   inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l9 .
eq p = r .
eq q = r .
-- check
red   inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l9 .
eq (p = r) = false .
eq q = r .
-- check
red   inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l9 .
eq (p = r) = false .
eq (q = r) = false .
-- check
red   inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l9 .
eq (q = r) = false .
eq p = r .
-- check
red   inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
eq (pc(s,r) = l10) = false .
-- check
red   inv10(s,p,q) implies   inv10(chnxt2(s,r),p,q) .
close

-- 12.2.1 pc(s,r) = l10, p = r, q = r
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l10 .
eq p = r .
eq q = r .
-- check
red   inv10(s,p,q) implies   inv10(chnxt2(s,r),p,q) .
close

-- -- 12.2.2 pc(s,r) = l10, (p = r) = false, q = r
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l10 .
eq (p = r) = false .
eq q = r .
-- check
red   ( inv10(s,p,q))  implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l10 .
eq (p = r) = false .
eq (q = r) = false .
-- check
red   inv10(s,p,q) implies   inv10(chnxt2(s,r),p,q) .
close

-- -- 12.2.4.1 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] :   inv10(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   inv10(s,p,q) implies   inv10(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] :   inv10(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   inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
eq (pc(s,r) = l11) = false .
-- check
red   inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l11 .
eq p = r .
eq q = r .
-- check
red   inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l11 .
eq (p = r) = false .
eq q = r .
-- check
red   inv10(s,p,q) implies   inv10(stlnx(s,r),p,q) .
close

-- -- 13.2.3.1a pc(s,r) = l11, (p = r) = false, (q = r) = false,next(s,r) = p,pc(s,p) = l6
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l11 .
eq (p = r) = false .
eq (q = r) = false .

eq next(s,r) = p .
eq pc(s,p) = l6 .
-- check
red   ( inv15(s,q,r) and  inv10(s,p,q)) implies   inv10(stlnx(s,r),p,q) .
close

-- -- 13.2.3.1b pc(s,r) = l11, (p = r) = false, (q = r) = false,next(s,r) = p,pc(s,p) != l6
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l11 .
eq (p = r) = false .
eq (q = r) = false .

eq next(s,r) = p .
eq (pc(s,p) = l6) = false .
-- check
red   (inv10(s,p,q)) implies   inv10(stlnx(s,r),p,q) .
close

-- -- 13.2.3.2 pc(s,r) = l11, (p = r) = false, (q = r) = false, next(s,r) != p
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l11 .
eq (p = r) = false .
eq (q = r) = false .

eq (next(s,r) = p) = false .
-- check
red   (inv10(s,p,q)) implies   inv10(stlnx(s,r),p,q) .
close

-- -- 13.2.4 pc(s,r) = l11,  p = r, (q = r) = false, pc(s,p) != l3
open INV .
-- fresh constants
op s : -> Sys .
ops p q r : -> Pid .
-- induction hypothesis
eq [:nonexec] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l11 .
eq (q = r) = false .
eq p = r .
-- check
red   inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
eq (pc(s,r) = l12) = false .
-- check
red   inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l12 .
eq p = r .
eq q = r .
-- check
red   inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l12 .
eq (p = r) = false .
eq q = r .
-- check
red   inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l12 .
eq (p = r) = false .
eq (q = r) = false .
-- check
red   inv10(s,p,q) implies   inv10(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] :   inv10(s,P:Pid,Q:Pid) = true .
-- assumptions
eq pc(s,r) = l12 .
eq (q = r) = false .
eq p = r .
-- check
red   inv10(s,p,q) implies   inv10(go2rs2(s,r),p,q) .
close