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Theorem imfiniobackwardinv-implies-leqrefine-aux
imfinbwsim(IOAut(cstart, cstep, cext), IOAut(astart, astep, aext), t, cINV, aINV) ⊦ C_≤T_A(IOAut(cstart, cstep, cext), IOAut(astart, astep, aext))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
imfiniobackwardinv-implies-leqrefine
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 122
Proof steps: 270
Used lemmas:
bwinv-leqstar
,
Used spec theorems:
IOrefine-def
/
leq-def
IOtrace
/
trace
IOrefine-conds
/
backwardsiminv-def
IOrefine-conds
/
proofobls-imfinbackwardsim
IOrefine-def
/
leqstar-def
IOtrace
/
fintrace
IOrefine-conds
/
proofobls-backwardsiminv
Koenigs-Lemma-gen
/
KoenigsLemma
Koenigs-Lemma-gen
/
infgraph-def
Koenigs-Lemma-gen
/
finroot-def
infgraph-gen
/
isroot-def
infgraph-gen-basic
/
edge-def
Koenigs-Lemma-gen
/
finout-def
Koenigs-Lemma-gen
/
allreachable-def
infgraph-gen
/
path-def
infgraph-gen
/
pathp-def
list-del
/
get-append-less
list-del
/
get-append-grt
IOtrace
/
infappend-moves-gen
IOtrace
/
preserve-INV
Used simplifier rules:
IO-Aut-data
/
sel-IOAut-dotstart
IOtrace
/
exec
IOtrace
/
tracestar-def
remtau
/
finremtau-def
stream-basic
/
sel-rqui-dotl
stream-basic
/
elim-finp-ant
stream
/
sel-fin
IOtrace
/
frag-finite-sl
IOtrace
/
finexec
stream-basic
/
sel-rqui0-dotf
stream-basic
/
elim-finp-suc
stream
/
sel-inf
IOtrace
/
frag-inf-sl
remtau
/
finremtau-one
infgraph-gen-basic
/
dom-def
set-basic
/
size-zero-01
set-basic
/
ne-01
nat-basic
/
l-02
nat-basic
/
a
nat-basic
/
c
set-basic
/
In-empty
set-basic
/
In-insert
nat
/
lels
nat-basic
/
f
nat
/
fle-01
nat-basic
/
s-04
nat-basic
/
refl-Nat
nat-basic
/
lf-01
nat-basic
/
lf-02
nat
/
le-ls-simp
nat-basic
/
ls-02
nat
/
elim-pred-c
nat-basic
/
oz
IOtrace
/
frag-step-inf-inf
nat-basic
/
eq-01
infgraph-gen-basic
/
edge-def
list-last
/
last-one
list
/
first
list
/
e
nat-basic
/
one-01
list-del
/
one-03
nat-inf
/
add-fin
stream
/
size-fin
list
/
len-02
nat-inf
/
add-ls-cancel-num-03
nat-inf
/
less-fin
nat-basic
/
less-zero
nat-inf
/
add-assoc
nat-inf
/
add-comm
nat-basic
/
succ
list-data
/
elim-add
list
/
a
stream
/
append-finfin
list
/
c
list
/
app-02
list-last
/
last-01
list
/
c-08
stream
/
append-assoc
stream
/
get-append2-fin
nat-inf
/
less-succ-leq
stream
/
size-append
stream
/
get-cons-succ
nat-inf
/
add-all-zero
nat-inf
/
add-ls-cancel-num-04
stream
/
get-append3-fin
nat-inf
/
num-add
nat-inf
/
ls-natinf-to-nat-1-2
list-del
/
get-append-less
nat-basic
/
zero
nat
/
add-num-03
list-del
/
get-append-grt
nat
/
l-num-01
nat
/
anti
nat
/
zero
nat
/
ler
list-del
/
get-butlast
nat
/
lels-03
list-data
/
l
list-last
/
l-02
list-getput
/
get-zero-01
nat-basic
/
nls-fst
list-del
/
get-last-04
list-del
/
get-last
nat-inf
/
less-inf2
stream
/
size-inf
nat-inf
/
disj-rqui-infty
nat-inf
/
addeqinf-cancel
nat-inf
/
inf-less
IOtrace
/
fragomega-def