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Theorem path-dups
⊦ path(x, H) ∧ dups(x) → cyclic(hd x, H)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
cyclic-weak-def
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 26
Proof steps: 60
Used lemmas:
cyclic-def
,
Used spec theorems:
list-del
/reflist/
dups-def
path-reachable
/
reach-n-path-n
list-last
/reflist/
l-02
list-del
/reflist/
firstn-last
path-reachable
/
path-prefix
list-del
/reflist/
firstn-restn-eq
Used simplifier rules:
nat-basic1
/
neq-01
nat-basic1
/
zero-01
list-last
/reflist/
l-02
nat-basic1
/
lf-02
list-data
/reflist/
size-01
nat
/
eqle-one
nat
/
let
nat-basic2
/
l-02
nat
/
ls-le-simp
nat
/
succ-01
nat-basic2
/
oz
list-del
/reflist/
get-succ
nat
/
elim-pred-c
nat
/
pred-03
list-del
/reflist/
firstN-empty
nat-basic2
/
eq-01
list-del
/reflist/
first-length
list
/reflist/
c-08
list-del
/reflist/
weak-firstN-rec
path-reachable
/
reachable-n-base
nat-basic1
/
zero
list-del
/reflist/
get-zero-01
nat
/
lels-03
nat
/
fle
nat
/
lels
nat-basic2
/
c
nat-basic2
/
a
nat-basic2
/
s
list
/reflist/
len-02
list
/reflist/
len
list
/reflist/
a
list
/reflist/
e-01
list
/reflist/
c
list-data
/reflist/
elim-list-c
list-data
/reflist/
l
nat-basic1
/
f