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Theorem from-append-add
⊦ ¬ # σ < ⌜n⌝ ∧ ¬ # σ0 < ⌜n1⌝ → ⌜σ to n⌝ + σ0 from n1 + n = σ0 from n1
Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 4
Proof steps: 9
Used lemmas:
get-from-01
,
sel-fin
,
from-fin
,
from-appfin
,
length-from
,
size-fin
,
get-from-inf
,
get-to
,
append-fininf
,
sel-inf
,
size-inf
,
from-inf
,
get-from
,
append-assoc
,
size-to
,
size-to-02
,
size-append
,
less-size-from
,
fin-size-from
,
extensionality
,
Used spec theorems:
list-del
/
get-append-grt
Used simplifier rules:
nat-inf
/
add-comm
nat-inf
/
add-assoc
nat-inf
/
disj-rqui-infty
nat-inf
/
addeqinf-cancel
nat-inf
/
inf-less
nat-inf
/
less-inf1
nat-inf
/
add-ls-cancel-01
nat-basic
/
c
nat-basic
/
a
nat-inf
/
add-fin
nat-inf
/
add-inf2
stream-basic
/
elim-finp-suc
nat-basic
/
l-02
nat
/
eq-01
list-data
/
l
nat-basic
/
f
nat
/
ls-le-simp
nat
/
lels
nat-basic
/
l
list
/
a
list
/
len
nat
/
ls
nat
/
le-ls-simp
nat
/
le-def
nat-inf
/
less-fin
nat
/
cancel-01
nat-inf
/
inj-rqui
nat-inf
/
sel-rqui-dotn
stream-basic
/
elim-finp-ant
list-del
/
get-append-less