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Theorem cyclic-floyd-def
⊦ cyclic(r, H) ↔ (∃ n, r0. n ≠ 0 ∧ reachable-n(H, n, r, r0) ∧ reachable-n(H, n + n, r, r0))
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: 29
Proof steps: 57
Used lemmas:
cyclic-def
,
cyclic-all-ncyclic
,
cyclic-ncyclic
,
cyclic-alt-def
,
Used spec theorems:
nat
/
one-02
nat-mult
/
zero-01
path-reachable
/
reachable-n-rec-1
path-reachable
/
reachable-n-trans
nat-mult
/
dist-merge
path-reachable
/
reach-n-split
Used simplifier rules:
nat-mult
/
ls-04
nat-mult
/
coef-21
nat-basic2
/
s
nat-basic1
/
ref-1
nat
/
le-add
nat-basic1
/
ls-02
nat
/
lels-03
path-reachable
/
reachable-n-trans
nat
/
cancel-01
nat-basic2
/
l
nat
/
lels
path-reachable
/
reachable-1-def
path-reachable
/
reachable-n-1
nat-mult
/
one-01
nat
/
lep-02
nat
/
add-num-01
nat-basic2
/
oz
nat-basic2
/
eq-01
nat-mult
/
rsucc-02
nat-basic2
/
succ
nat-mult
/
le-02
nat
/
lels-01
nat-basic1
/
f
nat-mult
/
ls-01
nat
/
elim-sub
nat-mult
/
two-zero-01
nat
/
elim-pred-c
path-reachable
/
reach-n-unique
nat
/
eq-01
nat-basic2
/
l-01
nat-mult
/
zero-01
nat-mult
/
one
nat-basic2
/
z
nat-mult
/
mult-c
nat-mult
/
mult-a
nat-mult
/
ax-03
path-reachable
/
reachable-n-base
nat-basic2
/
c
nat-basic2
/
a
nat-mult
/
two-02