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Theorem cyclic-alt-def
⊦ cyclic(r, H) ↔ (∃ m, r0. reachable-n(H, m, r, r0) ∧ (∃ n. n ≠ 0 ∧ (∀ n0. reachable-n(H, m + n0 * n, r, r0))))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
cyclic-floyd-def
,
cyclic-weak-def
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 8
Proof steps: 18
Used lemmas:
cyclic-def
,
Used spec theorems:
path-reachable
/
reach-n-split
Used simplifier rules:
nat-mult
/
one
path-reachable
/
reachable-n-trans
nat-mult
/
rsucc-02
nat-basic2
/
succ
nat-mult
/
ax-03
nat-mult
/
mult-a
nat-mult
/
mult-c
nat-basic2
/
z
nat-basic2
/
c
nat-basic2
/
a
nat-basic2
/
l-01
nat
/
lels-03
nat
/
lels-01
nat-basic1
/
ls-02
nat
/
elim-sub
path-reachable
/
reach-n-unique
nat-basic1
/
f