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Theorem insert-inset-after-retinsert
frag*(IOAut(setInit, setStep, setExt))(sl, AInvInsert(tid, e) + (al + ARetInsert(tid, true))), SetInv(sl.head.gstate, sl.head.lsf, sl.head.pcf), ¬ tid ∈ setExt !(al).map(.tid) ⊦ e ∈ sl.last.gstate.set
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
theorem-member-returns-true-after-insert
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 9
Proof steps: 29
Used lemmas:
inv-tid
,
frag-rely-inv
,
insert-inset-after-retinsert-ind
,
Used spec theorems:
IOtrace
/
finfrag-rec-end
Set
/
setStep
Set
/
gstepf-retInsert-RETINSERT
Used simplifier rules:
list
/
Last
list
/
c
IOtrace
/
not-finfrag-empty
list-last
/
last-elim
list
/
a
list
/
e
list
/
app-02
Set
/
elim-mkstate
list-data
/
elim-list-c
list
/
in-17
list
/
in-append
list
/
in-rec
list
/
in-14
list
/
in-15
list
/
c-06
Set
/
sel-mkstate-dotgstate
Set
/
sel-mkstate-dotlsf
Set
/
sel-mkstate-dotpcf
list
/
Nil
list
/
c-03
Set
/
inj-mkstate
Set
/
lstep
Set
/
pre-retMember
Set
/
disj-ARetInsert-ARetMember
Set
/
pre-retInsert
Set
/
inj-ARetInsert
Set
/
disj-invInsert-retInsert
Set
/
pre-invMember
Set
/
disj-ADoMember-ARetInsert
Set
/
pre-invInsert
Set
/
disj-ADoInsert-ARetInsert
Set
/
pre-idle
Set
/
disj-AInvInsert-ARetInsert
Set
/
disj-AInvMember-ARetInsert
set-basic
/
size-zero-01
set-basic
/
ne-01