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Theorem KoenigsLemma
infgraph(g), finroot(g), finout(g), allreachable(g) ⊦ ∃ nf. isroot(g)(nf(0)) ∧ pathp(g)(⌜nf⌝ )
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
weakfin-startfin-IObackward-INV-is-leqrefine
,
IOrefine-conds-imply-IOrefine
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 14
Proof steps: 30
Used lemmas:
KoenigsLemma-aux
,
it-succ
,
it-zero
,
allreachable-def
,
finout-def
,
finroot-def
,
infgraph-def
,
hpal-root
,
hpal-next
,
Used spec theorems:
infgraph-gen
/
pathp-def
Used simplifier rules:
list-del
/
one-03
nat-basic
/
c
nat-basic
/
a
stream
/
sel-inf
nat-inf
/
add-comm
nat-inf
/
add-assoc
nat-inf
/
disj-rqui-infty
nat-inf
/
addeqinf-cancel
nat-inf
/
inf-less
stream
/
size-inf
nat-inf
/
add-fin
nat-inf
/
less-inf2
nat-basic
/
l
nat-basic
/
s-04
stream
/
sel-fin
nat-inf
/
less-fin
stream
/
size-fin
nat-inf
/
ls-natinf-to-nat-2-1
nat-basic
/
refl-Nat
list-data
/
size-nil
nat-basic
/
z-01
list
/
a
list
/
in-17
list
/
in-append
list-del
/
get-last
stream
/
append-finfin
list-last
/
last-def
list
/
in-15
stream
/
append-assoc
stream
/
get-append2-fin
nat-inf
/
less-succ-leq
list
/
len-02
stream
/
size-append
list-del
/
get-butlast
nat-inf
/
add-all-zero
nat-inf
/
add-ls-cancel-num-04