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Theorem hpal-next-auxh
∀ b. b ∈ s → ¬ haspathanylength(g)(b) ⊦ ∃ n. ∀ x. pathp(g)(⌜x⌝ ) ∧ x ≠ [] ∧ x.head ∈ s → # x < n
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
hpal-next-aux
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 31
Proof steps: 77
Used lemmas:
haspathanylength-def
,
Used spec theorems:
infgraph-gen
/
pathp-def
list-del
/
get-append-less
Used simplifier rules:
set-basic
/
In-empty
set-basic
/
In-insert
set-basic
/
size-zero-01
set-basic
/
ne-01
nat-basic
/
succ
nat-basic
/
f
list-data
/
l
nat-basic
/
trans-Nat
nat-basic
/
lf
nat-basic
/
c
nat-basic
/
a
nat-basic
/
s-04
list-data
/
elim-list-c
nat
/
fle
nat
/
lels
nat-basic
/
ls-02
nat-basic
/
l
list
/
a
list
/
len-05
list
/
c
stream
/
append-finfin
list
/
e
list
/
app-02
stream
/
to-succ-cons-l-lem
nat-basic
/
eq-01
list-del
/
firstn-length-04
list
/
c-08
list-del
/
elim-firstn-restn
list
/
len
stream
/
append-assoc
nat
/
lep
stream
/
sel-fin
stream
/
get-cons-succ
stream
/
get-append2-fin
nat-inf
/
add-comm
nat-inf
/
add-assoc
nat-inf
/
less-fin
nat-inf
/
add-all-zero
nat-inf
/
add-ls-cancel-num-04
stream
/
size-fin
list
/
len-02
stream
/
size-append
nat-inf
/
add-fin
nat-inf
/
less-succ-leq
stream
/
get-append3-fin
nat-inf
/
ls-natinf-to-nat-2-1
nat-inf
/
ls-natinf-to-nat-1-2
nat-basic
/
l-02
nat-basic
/
one-01
list-del
/
one-03
nat
/
lez
list-del
/
get-zero
list-del
/
get-append-grt
nat-basic
/
oz
nat
/
succ-01
list-del
/
get-append-less
list-del
/
get-succ
nat
/
elim-pred-c
nat
/
fle-01
nat-basic
/
lf-02
nat-basic
/
zero
list-getput
/
get-zero-01
nat-basic
/
l-08
nat-basic
/
nls-fst
nat-basic
/
l-05
nat
/
let
nat
/
le-ls-simp