--> I. Base case
open BASE-QLOCK
-- check
  red inv1(init,i,j) .
close

--> II. Induction case
--> 1. want(s,k)
open ISTEP-QLOCK
-- fresh constants
  op k : -> Pid .
-- assumptions
  -- eq c-want(s,k) = true .
  eq pc(s,k) = rm .
-- successor state
  eq s' = want(s,k) .
-- check
  red istep1 .
close
open ISTEP-QLOCK
-- fresh constants
  op k : -> Pid .
-- assumptions
  eq c-want(s,k) = false .
-- successor state
  eq s' = want(s,k) .
-- check
  red istep1 .
close
--> 2. try(s,k)
open ISTEP-QLOCK
-- fresh constants
  op k : -> Pid .
  op q : -> Queue .
-- assumptions
  -- eq c-try(s,k) = true .
  eq pc(s,k) = wt .
  eq queue(s) = q , k .
-- successor state
  eq s' = try(s,k) .
-- check
  red istep1 .
close
open ISTEP-QLOCK
-- fresh constants
  op k : -> Pid .
-- assumptions
  eq c-try(s,k) = false .
-- successor state
  eq s' = try(s,k) .
-- check
  red istep1 .
close
--> 3. exit(s.k)
open ISTEP-QLOCK
-- fresh constants
  op k : -> Pid .
-- assumptions
  -- eq c-exit(s,k) = true .
  eq pc(s,k) = cs .
-- successor state
  eq s' = exit(s,k) .
-- check
  red istep1 .
close
open ISTEP-QLOCK
-- fresh constants
  op k : -> Pid .
-- assumptions
  eq c-exit(s,k) = false .
-- successor state
  eq s' = exit(s,k) .
-- check
  red istep1 .
close

--> QED