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Theorem abs-is-fwsim
⊦ fwsim(HashsetIOA, SetIOA, λ as, cs. abs(cs, as) ∧ SetInv(as.gstate, as.lsf, as.pcf) ∧ HashsetInv(cs.gstate, cs.lsf, cs.pcf))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Hashset-fwsim-Set
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 22
Proof steps: 48
Used lemmas:
ext-RetMember
,
ext-RetInsert
,
ext-InvMember
,
ext-InvInsert
,
ext-DoMember
,
ext-DoInsert
,
ext-tau
,
HashsetIOA-def
,
Used spec theorems:
Set-Test-IOAut
/
SetIOA-def
IOforward
/
proofobls-forwardsim
Hashset-proofs
/
init-state-inv
Hashset-refines-Set
/
abs-init
Set-proofs
/
init-state-inv
Hashset-proofs
/
HashsetInv-thm
Hashset-refines-Set
/
abs-theorem
IOtrace
/
move
Used simplifier rules:
remtau
/
finremtau-one
Hashset
/
sel-mkstate-dotpcf
Hashset
/
sel-mkstate-dotlsf
Hashset
/
sel-mkstate-dotgstate
nat-basic
/
zero
nat
/
gr-def
Hashset
/
hashsetInit
Hashset-refines-Set
/
gabs-def
Hashset-refines-Set
/
abs-def
Set
/
setInit
Set
/
sel-mkstate-dotpcf
Set
/
sel-mkstate-dotlsf
Set
/
sel-mkstate-dotgstate
IOtrace
/
move-empty
opt
/
elim-rqui
opt
/
disj-rqui-tau
Hashset-refines-Set
/
ren-retMEMBER
Set
/
disj-ARetMember-tau
Hashset-refines-Set
/
ren-retINSERT
Set
/
disj-ARetInsert-tau
Hashset-refines-Set
/
ren-invMEMBER
Set
/
disj-AInvMember-tau
Hashset-refines-Set
/
ren-invINSERT
Set
/
disj-AInvInsert-tau
Hashset-refines-Set
/
ren-doMEMBER
Set
/
disj-ADoMember-tau
Hashset-refines-Set
/
ren-doINSERT
Set
/
disj-ADoInsert-tau
Hashset-refines-Set
/
ren-tau
Set-proofs
/
SetInv-thm
IO-Aut-data
/
sel-IOAut-dotext
Set
/
inj-mkstate
list
/
a
list-last
/
last-def
list-del
/
get-zero
IOtrace
/
finfrag-two
Set-Test-IOAut
/
ext-RetMember
opt
/
sel-rqui-dote
list
/
c-04
Set-Test-IOAut
/
ext-RetInsert
Set-Test-IOAut
/
ext-InvMember
Set-Test-IOAut
/
ext-InvInsert
Set-Test-IOAut
/
ext-DoMember
Set-Test-IOAut
/
ext-DoInsert
list
/
e