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Theorem cyclic-weak-def
⊦ cyclic(r, H) ↔ (∀ n. ∃ r0. reachable-n(H, n, r, r0))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
cyclic-brent-def
,
legal-noncylic-equiv-reaches-null
,
Used by units in proved state:
challenge4
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 9
Proof steps: 23
Used lemmas:
path-nodups-subset
,
path-dups
,
cyclic-alt-def
,
Used spec theorems:
path-reachable
/
reach-n-split
path-reachable
/
reach-n-path-n
Used simplifier rules:
list-dup
/reflist/
dups-cons
nat
/
succ-01
nat-basic1
/
lf-02
nat-basic1
/
f
store
/linheap/
empty
nat-basic2
/
l-02
list
/reflist/
c-08
list-dup
/reflist/
rec
list
/reflist/
e-01
nat
/
add-num-01
list
/reflist/
a
list
/reflist/
len-02
list
/reflist/
len
list
/reflist/
c
list-data
/reflist/
size-01
list-data
/reflist/
elim-list-c
nat-mult
/
le-01
nat
/
lels-01
nat-mult
/
ls-08
nat
/
elim-sub
path-reachable
/
reachable-n-base
nat-basic2
/
z
nat-basic2
/
z-01
nat
/
le-add
nat-mult
/
mult-c
nat-mult
/
mult-a
nat-mult
/
rsucc-02
nat-basic2
/
c
nat-basic2
/
a
nat-basic2
/
oz
nat-basic2
/
succ
nat
/
lels