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Theorem cyclic-brent-def
⊦ cyclic(r, H) ↔ (∃ n, m, r0. m ≠ 0 ∧ m ≤ 2 ^ n ∧ reachable-n(H, 2 ^ n - 1, r, r0) ∧ reachable-n(H, m, r0, 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: 16
Proof steps: 42
Used lemmas:
cyclic-weak-def
,
cyclic-all-ncyclic
,
cyclic-def
,
Used spec theorems:
path-reachable
/
reach-n-split
path-reachable
/
reach-n-split-le
nat-pot
/
potex
Used simplifier rules:
path-reachable
/
reachable-n-trans
nat-basic2
/
succ
nat-basic1
/
trans-1
nat-basic1
/
lf
nat-pot
/
pot-mon
nat-mult
/
ls
nat
/
ls-le-simp
nat
/
lez-01
path-reachable
/
reachable-n-base
nat-mult
/
two-zero-01
nat
/
fle-01
nat-pot
/
add
nat-pot
/
pot2-def
nat
/
eq-01
nat
/
lep
nat-mult
/
mult-c
nat-mult
/
mult-a
nat-mult
/
one
nat-basic2
/
l-02
nat-basic1
/
lf-02
nat
/
fle
nat-basic2
/
z
nat
/
add-01
nat
/
le-ls-simp
nat
/
lels
nat-basic2
/
s
nat-basic2
/
oz
nat-basic1
/
lf-01
nat
/
elim-pred-c
nat-pot
/
two-pot-zero
nat
/
ax-02
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