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Theorem abs-init
hashsetInit(mkstate(gs, lsf, pcf)), HashsetInv(gs, lsf, pcf) ⊦ ∃ ags, alsf, apcf. setInit(mkstate(ags, alsf, apcf)) ∧ abs(mkstate(gs, lsf, pcf), mkstate(ags, alsf, apcf))
Type: A proof obligation
Validity: The proof is valid.
Features:
Comment:
Used by:
abs-theorem
,
Used by units in proved state:
Hashset-refines-Set-Theory-Instance
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 2
Proof steps: 8
Used lemmas:
labs-def
,
gabs-def
,
abs-def
,
Used spec theorems:
abs
/
absset-def
Used simplifier rules:
Set
/
setInit
Set
/
sel-mkgs-dotset
Set
/
sel-mkls-dottid
nat-basic
/
zero
nat
/
gr-def
Hashset
/
hashsetInit
set-basic
/
In-empty
hashset-preds
/
size-mkar
hashset-preds
/
get-mkar
Set
/
disj-idle-invInsert
Set
/
disj-idle-invMember
Hashset
/
disj-M8-idle
Hashset
/
disj-M15-idle
Hashset
/
disj-M11-idle
Hashset
/
disj-M16-idle
Hashset
/
disj-M12-idle
Hashset
/
disj-M9-idle
Hashset
/
disj-M14-idle
Hashset
/
disj-M13-idle
Hashset
/
disj-M10-idle
Hashset
/
disj-M7-idle
Hashset
/
disj-M17-idle
Hashset
/
disj-M6-idle
Hashset
/
disj-M5-idle
Hashset
/
disj-M4-idle
Hashset
/
disj-M3-idle
Hashset
/
disj-M2-idle
Hashset
/
disj-M1-idle
Hashset
/
disj-I21-idle
Hashset
/
disj-I5-idle
Hashset
/
disj-I19-idle
Hashset
/
disj-I15-idle
Hashset
/
disj-I9-idle
Hashset
/
disj-I14-idle
Hashset
/
disj-I13-idle
Hashset
/
disj-I8-idle
Hashset
/
disj-I7-idle
Hashset
/
disj-I20-idle
Hashset
/
disj-I18-idle
Hashset
/
disj-I17-idle
Hashset
/
disj-I16-idle
Hashset
/
disj-I12-idle
Hashset
/
disj-I11-idle
Hashset
/
disj-I10-idle
Hashset
/
disj-I6-idle
Hashset
/
disj-I4-idle
Hashset
/
disj-I3-idle
Hashset
/
disj-I2-idle
Hashset
/
disj-I1-idle