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Theorem valid-eraseq-stronger-next-append-none
m < # apebs ⊦ valid-eraseq-stronger(subarray(apebs, 0, m), q) → (valid-eraseq-stronger(subarray(apebs, 0, m + 1), q + eq-entry(m, none) ') ↔ ¬ valid-peb(apebs[m]))
Type: A user defined theorem
Validity: The proof is valid.
Features: ss,
Comment:
Used by:
Used by units in proved state:
ubi-asm
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 5
Proof steps: 17
Used lemmas:
valid-eraseq-stronger-rec
,
valid-eraseq-stronger-base
,
valid-eraseq-stronger-one
,
Used spec theorems:
erasequeue
/
in-append
array-copy
/apebs/
subarray-at
Used simplifier rules:
list
/erasequeue-base/
Nil
nat-basic
/
f
nat
/
lels-03
array-copy
/apebs/
subarray-at
sqns
/
valid-sqns-rec
sqns
/
valid-sqns-subarray
nat
/
ls-le-simp
nat
/
lels
nat
/
succ-01
array-copy
/apebs/
size-subarray
list
/erasequeue-base/
a
list
/erasequeue-base/
c
erasequeueentry
/
elim
nat-basic
/
succ
oelem
/nat-set/
transitivity
nat-basic
/
lf
apeb
/
elim
nat-basic
/
neq-04
oelem
/nat-set/
sls
apeb
/
inj
oelem
/nat-set/
ls-le
nat-basic
/
s-04
nat-basic
/
add-base
valid-peb
/
valid-peb-imp-valid-peb0
bag-union
/nat-bag/
union-empty
bag-union
/nat-bag/
union-ass
bag-union
/nat-bag/
union-com
nat-basic
/
lf-02
nat-basic
/
lf-01
oelem
/nat-set/
irreflexivity
array-copy
/apebs/
subarray-elim
nat-basic
/
a
nat-basic
/
c
nat-basic
/
succ-03
nat-basic
/
ls-02