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Theorem legal-noncylic-equiv-reaches-null
legal(H), r ∈ H, r ≠ null ⊦ ¬ cyclic(r, H) ↔ (∃ r0. reachable(r, r0, H) ∧ H[r0] .nxt = null)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
challenge4
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 20
Proof steps: 37
Used lemmas:
legal-nxt-1
,
cyclic-weak-def
,
Used spec theorems:
path-reachable
/
reachable-1-def
path-reachable
/
reach-n-path-n
path-reachable
/
k-reachable-def
path-reachable
/
reachable-star-def
path-reachable
/
reachable-n-rec-rev
Used simplifier rules:
path-reachable
/
reachable-1-def
path-reachable
/
reach-n-unique
path-reachable
/
reach-alloc
list
/reflist/
e-02
path-reachable
/
path-last-not-null
list-last
/reflist/
last-elim
list-last
/reflist/
l-02
list-data
/reflist/
l
path-reachable
/
path-last
list
/reflist/
e-01
nat-basic2
/
eq-01
list
/reflist/
a
list
/reflist/
len-02
list
/reflist/
len
list
/reflist/
c
list-data
/reflist/
size-01
nat-basic2
/
oz
nat-basic2
/
a
nat-basic2
/
c
list-data
/reflist/
elim-list-c
path-reachable
/
id-reachable
nat-basic2
/
succ
path-reachable
/
reachable-n-base