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Theorem theorem-allinserts-finished-false-implies-notin
exec*(IOAut(setInit, setStep, setExt))(sl, al), ∀ tid, al1, al2. al = al1 + (AInvInsert(tid, e) + al2) → (∃ al3, al4. al2 = al3 + (ARetInsert(tid, false) + al4) ∧ ¬ tid ∈ setExt !(al3).map(.tid)) ⊦ ¬ e ∈ sl.last.gstate.set
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 3
Proof steps: 14
Used lemmas:
allinserts-finished-false-implies-notin-ind
,
Used spec theorems:
list-del
/
get-last-nonempty
Used simplifier rules:
set-basic
/
size-zero-01
set-basic
/
ne-01
list
/
a
list
/
c
IO-Aut-data
/
sel-IOAut-dotstart
IOtrace
/
finexec
Set
/
elim-mkstate
nat-basic
/
c
nat-basic
/
a
nat-basic
/
refl-Nat
nat-basic
/
s-04
nat
/
ls-01
IOtrace
/
not-finfrag-empty
list-data
/
l
nat-basic
/
one-01
nat
/
le-def
nat
/
elim-pred-c
list-getput
/
get-zero-01
list-data
/
elim-add
list
/
e
list
/
app-02
nat-basic
/
eq-01
nat-basic
/
succ
list
/
len-05
nat
/
add-01
nat-basic
/
add-base
nat-basic
/
zero
nat-basic
/
oz
Set
/
inj-mkstate