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Theorem is-encoded-split-one
⊦ is-encoded(ns, buf0) ∧ is-encoded(n, buf1) ∧ ¬ n ∈ ns → (is-encoded(ns1, buf0 + buf1) ↔ ns1 = ns ++ n)
Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by:
Used by units in proved state:
persistence-io-asm
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 16
Proof steps: 38
Used lemmas:
is-encoded-unique
,
is-encoded-base
,
is-encoded-rec
,
is-encoded-size
,
Used spec theorems:
set-basic
/nat-set/
Size-insert
set-basic
/nat-set/
Extension
Used simplifier rules:
array-splice
/buffer/
append-eq-emptyar
set-basic
/nat-set/
size-zero
nat
/
elim-pred-c
array-splice
/buffer/
append-right-size0
nat-basic
/
eq-02
array
/buffer/
Size-mkarray
nat-basic
/
z-01
set-union
/nat-set/
del-e-02
set-union
/nat-set/
del-size-02
array-splice
/buffer/
append-inj
encoding
/encoding-nat/
is-encoded-prefix
nat
/
le-num-03
nat
/
ls-01
nat
/
lels
nat
/
lep-02
set-union
/nat-set/
del-feq
set-basic
/nat-set/
ne
set-basic
/nat-set/
Size-empty
nat-mult
/
zero
set-basic
/nat-set/
In-empty
array-splice
/buffer/
append-left-size0
set-union
/nat-set/
del-addeq-05
set-union
/nat-set/
del-e-01
array-splice
/buffer/
append-zero-right
set-basic
/nat-set/
size-zero-01
set-basic
/nat-set/
ne-01
encoding-fixed-size
/encoding-nat/
is-encoded-size
nat-basic
/
eq-01
nat-mult
/
rsucc-02
nat
/
add-01
nat-basic
/
add-base
nat-mult
/
zero-02
set-basic
/nat-set/
Size-insert
set-union
/nat-set/
del-size
nat-basic
/
l
nat
/
le-def
nat-basic
/
nls-fst
nat
/
ls
nat-basic
/
f
nat-basic
/
lf-02
nat-basic
/
lf-01
nat-basic
/
oz
nat-basic
/
s-04
nat-basic
/
c
nat-basic
/
a
nat-mult
/
mult-c
nat-mult
/
mult-a
encoding-fixed-size
/encoding-nat/
encoding-requires-space
nat-mult
/
coef-17
array-splice
/buffer/
append-len
encoding
/encoding-nat/
is-encoded-unique
array-splice
/buffer/
append-a
set-union
/nat-set/
Delete
set-basic
/nat-set/
In-insert