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Theorem add-preserves-reachable-rev
⊦ H[r1].nxt = H[r2].nxt ∧ r0 ≠ r2 ∧ ce.nxt = r2 ∧ ¬ reachable(r, r0, H) ∧ ¬ reachable(r, r2, H) ∧ r2 ≠ null ∧ r2 ∈ H ∧ reachable(r, r1, H) → (reachable(r, r0, H[r1, ce]) ↔ false)
Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 29
Proof steps: 55
Used lemmas:
fromnext-reachable-rev
,
startnotinH-notreachable
,
reachnext
,
fromnext-reachable
,
path-two
,
reach-reachnext
,
reachable-notnullinH
,
path-cons
,
self-reachable
,
path-one
,
reachable-def
,
reach-alloc
,
Used spec theorems:
store
/linheap/
At-other
Used simplifier rules:
store
/linheap/
in-neq
list-last
/reflist/
l-02
list
/reflist/
c
list-last
/reflist/
l-05
store
/linheap/
k-At-same
list
/reflist/
app
list-last
/reflist/
l
list-last
/reflist/
last-def
store
/linheap/
At-same
store
/linheap/
insin
store
/linheap/
In-insert
list
/reflist/
a