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Theorem hpal-reachset-set
finout(g), ∀ a. a ∈ s → ¬ haspathanylength(g)(a) ⊦ ∃ s0. ∀ b. (∃ a. a ∈ s ∧ path(g)(a, b)) ↔ b ∈ s0
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
hpal-root
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 36
Proof steps: 88
Used lemmas:
reach-def
,
reachle-def
,
finreachle-fin
,
haspathanylength-def
,
finout-def
,
Used spec theorems:
infgraph-gen
/
path-def
infgraph-gen
/
pathp-def
list-del
/
get-append-less
list-del
/
get-append-grt
list-del
/
get-firstn
Used simplifier rules:
set-basic
/
size-zero-01
set-basic
/
ne-01
set-union
/
del-size
nat
/
le-def
nat-basic
/
one-01
nat
/
ls-01
nat-basic
/
s-04
nat-basic
/
refl-Nat
nat-basic
/
a
nat-basic
/
c
set-union
/
Delete
set-union
/
unc
set-union
/
una
set-union
/
Union
list-data
/
elim-list-c
list
/
c
list
/
a
stream
/
append-finfin
list
/
e
list
/
app-02
list-last
/
l-02
list-data
/
l
nat-basic
/
f
nat
/
ls-le-simp
stream
/
to-succ-cons-l-lem
nat-basic
/
eq-01
nat-basic
/
succ
list-del
/
firstn-length-03
list
/
len-05
list
/
c-08
stream
/
append-assoc
stream
/
get-append2-fin
nat-inf
/
add-comm
nat-inf
/
add-assoc
nat-inf
/
less-fin
nat-inf
/
less-succ-leq
stream
/
size-fin
list
/
len-02
stream
/
size-append
stream
/
sel-fin
stream
/
get-cons-succ
nat-inf
/
add-all-zero
nat-inf
/
add-ls-cancel-num-04
nat-inf
/
add-fin
nat
/
fle-01
nat
/
lels
nat
/
elim-pred-c
nat-basic
/
trans-Nat
nat-basic
/
lf
nat
/
succ-01
nat-basic
/
oz
nat
/
lels-03
list-del
/
get-succ
list-del
/
one-03
nat-basic
/
zero
nat
/
lez
nat-basic
/
lf-02
nat-basic
/
less-zero
list-del
/
get-zero
list-del
/
get-append-less
list-del
/
get-append-grt
nat-basic
/
nls-fst
nat
/
lels-02
list-data
/
elim-add
set-basic
/
In-empty