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Theorem frag-rely-inv
SetInv(sl.head.gstate, sl.head.lsf, sl.head.pcf), frag*(IOAut(setInit, setStep, setExt))(sl, al) ⊦ sl.head.gstate.set ⊆ sl.last.gstate.set ∧ SetInv(sl.last.gstate, sl.last.lsf, sl.last.pcf)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
allinserts-finished-false-implies-notin-ind
,
frag-subset
,
insert-inset-after-retinsert
,
insert-inset-after-retinsert-ind
,
inset-member-returns-true
,
inset-member-returns-true-ind
,
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: 14
Proof steps: 32
Used lemmas:
inv-tid
,
Used spec theorems:
IOtrace
/
finfrag-rec
Set-proofs
/
SetInv-thm
Set
/
setStep
Set
/
gstepf-invInsert-DOINSERT
Set
/
gstepf-invMember-DOMEMBER
Set
/
gstepf-retInsert-RETINSERT
Set
/
gstepf-retMember-RETMEMBER
Used simplifier rules:
IOtrace
/
not-finfrag-empty
list-data
/
elim-list-c
list
/
c
list
/
a
list
/
e
list
/
app-02
Set
/
elim-mkstate
IOtrace
/
finfrag-onlyone
list
/
c-08
list
/
c-03
list
/
app
list-last
/
last-one
Set
/
inj-mkstate
set-basic
/
subsize-eq-01
list-last
/
last-rec
Set-proofs
/
SetInv-thm
set-basic
/
sub-ntrans-01
Set
/
lstep
Set
/
pre-idle
Set
/
gstepf-idle
Set
/
pre-invInsert
Set
/
updsel--dotset-dotset
set-basic
/
sub-add-03
Set
/
pre-invMember
Set
/
pre-retInsert
Set
/
pre-retMember