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Theorem reachable-addnew-rev
⊦ ¬ r2 ∈ H ∧ r ∈ H ∧ ¬ reachable(r, r1, H) → (reachable(r, r1, H[r2, ce]) ↔ (∃ r0. reachable(r, r0, H) ∧ H[r0].nxt = r2 ∧ r2 ≠ null ∧ (r1 = r2 ∨ reachable(ce.nxt, r1, H))))
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: 42
Proof steps: 80
Used lemmas:
null-not-reachable
,
reachable-notnullinH
,
path-two
,
reach-reachnext
,
reachable-addnew
,
reachable-trans
,
path-prefix
,
path-postfix
,
startnotinH-notreachable
,
path-cons
,
reachable-def
,
path-last
,
path-new-irrelevant-strong
,
path-split-last
,
path-one
,
reachable-nodups-def
,
endnotinH-notreachable
,
reach-alloc
,
Used spec theorems:
store
/linheap/
In-insert
list
/reflist/
In
store
/linheap/
At-other
list-last
/reflist/
lapp
Used simplifier rules:
list-last
/reflist/
l-02
list-last
/reflist/
last-elim
list-dup
/reflist/
f
list-last
/reflist/
l-in
list
/reflist/
in-rec
list-last
/reflist/
lapp-01
list-dup
/reflist/
e-01
list
/reflist/
in-empty
store
/linheap/
At-other
list
/reflist/
Nil
list-dup
/reflist/
rec
list-dup
/reflist/
l-03
list
/reflist/
in-17
list
/reflist/
in-append
list
/reflist/
e-02
list-last
/reflist/
l
list-dup
/reflist/
a
list-dup
/reflist/
c-02
list-dup
/reflist/
f-01
list
/reflist/
in-06
store
/linheap/
In-insert
list
/reflist/
app
list-last
/reflist/
last-def
list
/reflist/
c
list
/reflist/
a
store
/linheap/
At-same
list-last
/reflist/
l-05
store
/linheap/
in-neq
store
/linheap/
At-in-out
store
/linheap/
insin