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Theorem acyclic-rem-not-reachable
∀ r. r ∈ h → ¬ reachable(h[r].nxt, r, h), reachable(r, r0, h), h[r0].nxt ≠ null, h[r0].nxt ∈ h, ce.nxt = h[h[r0].nxt].nxt ⊦ ¬ reachable(r, h[r0].nxt, h[r0, ce])
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: 34
Proof steps: 70
Used lemmas:
path-split-last
,
linearity-path
,
path-postfix
,
reachable-def
,
path-modify
,
path-cons
,
self-reachable
,
path-two
,
reach-alloc
,
path-one
,
reachable-nodups-def
,
Used spec theorems:
list-last
/reflist/
lapp
list
/reflist/
lastoc-rew
Used simplifier rules:
list
/reflist/
a
list-dup
/reflist/
rec
list
/reflist/
in-empty
list-dup
/reflist/
e-01
list
/reflist/
app
list-last
/reflist/
last-one
list-last
/reflist/
last-elim
list
/reflist/
in-17
list
/reflist/
in-append
list-dup
/reflist/
f
list
/reflist/
e-02
list
/reflist/
in-rec
list-dup
/reflist/
f-01
store
/linheap/
At-same
store
/linheap/
in-neq
store
/linheap/
insin
list
/reflist/
Nil
list
/reflist/
in-06
list
/reflist/
c
list
/reflist/
in-01
list-last
/reflist/
last-01
list-dup
/reflist/
a
list
/reflist/
app-04
list
/reflist/
app-01
list
/reflist/
app-03
list
/reflist/
app-06
list
/reflist/
in-15
list
/reflist/
inex
list
/reflist/
in-16
list
/reflist/
in-14
list
/reflist/
neq-03
list
/reflist/
c-03
list-last
/reflist/
last-def
list
/reflist/
c-06
list
/reflist/
Last