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Theorem infappend-moves-gen
start(sf(0)), ∀ n. move(IOAut(start, step, ext))(sf(n), cext !(caf(n) '), sf(n + 1)) ⊦ trace(IOAut(start, step, ext))(cext !(⌜caf⌝ ))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
infappend-moves
,
Used by units in proved state:
IOrefine-conds-imply-IOrefine
,
weakfin-startfin-IObackward-INV-is-leqrefine
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 181
Proof steps: 343
Used lemmas:
move
,
frag-inf-al
,
frag-finite-al
,
fragstar
,
frag
,
exec
,
trace
,
not-finfrag-empty
,
Used spec theorems:
infinite-append
/
infinite-append
infinite-append
/
infinite-append-butlast
list-getput
/
get-zero-01
remtau
/
remtau-empty-equiv
remtau
/
remtau-split-list-weak
remtau
/
remtau-append
stream
/
extensionality-to
remtau
/
remtau_of_to-to_of_rmtau
stream
/
appinf-to-ge
stream
/
extensionality
stream
/
prefix-def
stream
/
to-unwind-end-inf
list-getput
/
extension
remtau
/
remtau-split-list-inf
stream
/
append-le-to
stream
/
from-append-tofrom
stream
/
swap-from-to
stream
/
get-finto
stream
/
get-to
Used simplifier rules:
stream-basic
/
inj-rqui
remtau
/
finremtau-def
list-data
/
elim-add
list
/
a
list
/
in-14
list
/
c
nat-basic
/
a
nat-basic
/
c
nat-inf
/
add-fin
IO-Aut-data
/
sel-IOAut-dotstart
nat-inf
/
inj-rqui
stream
/
size-fin
stream-basic
/
test-finp-rqui
stream
/
to-fin
nat-basic
/
s-04
nat-inf
/
inf-inseq-reduce
nat-inf
/
add-assoc
nat-inf
/
add-comm
stream
/
from-fin
nat-inf
/
less-fin
stream
/
size-inf
nat-inf
/
addeqinf-cancel
nat-inf
/
disj-rqui-infty
nat-basic
/
eqs
nat-inf
/
eq-natinf-to-nat-2-1
stream
/
fin-finlen-tolen
stream-basic
/
disj-rqui-rqui0
stream
/
elim-fromto-inf
stream
/
append-assoc
stream
/
appendend-equal
remtau
/
remtau-append
stream
/
appinf-selfun
nat-inf
/
less-inf2
stream
/
sel-inf
remtau
/
remtau-one
stream
/
appinf-get-ge-01
remtau
/
finremtau-append
stream
/
appinf-to-ge-01
option
/
elim-Some
option
/
disj-Some-None
stream
/
infapp-embed
stream
/
appinf-sel
remtau
/
finremtau-one
nat
/
lep
list
/
app-04
remtau
/
finremtau-empty
list
/
e
stream
/
to-inf
stream
/
from-inf
stream-basic
/
elim-finp-suc
stream-basic
/
test-finp-rqui0
nat-inf
/
less-inf1
nat-inf
/
add-inf2
stream
/
leq-symm-2
stream
/
neq-fin-inf-03
stream
/
append-empty
nat-basic
/
f
nat
/
fle-01
list-data
/
l
nat-basic
/
lf-01
stream
/
size-append
stream
/
append-to-size-01
stream
/
append-to-gr-01
nat-basic
/
eq-01
list
/
app-02
stream
/
to-empty-inf
list
/
len
stream
/
size-inf-to
nat-basic
/
l-01
stream
/
append-finfin
stream
/
leq-append-right
nat
/
lels-03
nat
/
elim-sub
stream
/
size-succ
stream
/
sel-fin
nat-inf
/
add-cancel-03
nat-inf
/
sum-zero-fin
stream-basic
/
inj-rqui0
stream
/
append-inf
list
/
in-15
list
/
app-06
stream
/
size-to
stream
/
get-to
stream
/
empty
stream
/
leq-empty
stream
/
append-split-fin
stream
/
size-empty-equiv
stream
/
to-to-eq-inf
stream
/
append-gr-to
stream-basic
/
sel-rqui-dotl
nat
/
zero
stream
/
to-zero
list
/
app
stream
/
to-zero-nf
nat-basic
/
succ
stream-basic
/
elim-finp-ant
nat
/
fle
nat
/
lels
nat
/
le-ls-simp
IO-Aut-data
/
sel-IOAut-dotstep
list-del
/
first-length
nat
/
ls-01
nat
/
le-def
nat-basic
/
l-06
nat-basic
/
l
nat-basic
/
lf-02
nat-basic
/
l-02
nat-basic
/
ls-02
list-getput
/
get-zero-01
nat-basic
/
z-01
nat
/
elim-pred-c
nat-basic
/
oz
list-del
/
list-select-not-first
stream
/
length-from
nat-basic
/
lf
nat-basic
/
trans-Nat
nat-basic
/
l-05
nat
/
ls-add-not-01
nat
/
succ-01
stream
/
get-finto
nat
/
ls-le-simp
stream
/
get-from-01
nat
/
eqle-one
nat
/
lep-02
nat
/
let
nat
/
ls-03
nat-basic
/
one-01
nat-basic
/
refl-Nat
stream
/
get-from-inf
stream
/
get-infto
nat
/
add-num-03
nat
/
les
nat-basic
/
add-base
nat
/
add-01
nat-basic
/
zero
list-data
/
size-nil
list
/
len-05
list-del
/
get-numrec
list
/
c-08
list-last
/
last-elim
stream
/
from-zero
nat-inf
/
not-less-zero
nat-inf
/
ls-trans
IO-Aut-data
/
sel-IOAut-dotext