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Theorem prepost-wl-free-max-below
∃ m. m < # wlar ∧ wlar[m].ec < n ∧ wlar[m].status = free ⊦ ⟪ubi_wl_find_free_max_below#(n, wlar; m)⟫ (m < # wlar ∧ wlar[m].status = free ∧ wlar[m].ec = below(free-ecs(wlar), n).max)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
prepost-get-peb
,
prepost-get-pebs-for-wl
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 15
Proof steps: 48
Used lemmas:
find-max-below
,
Used spec theorems:
wlarray
/
free-ecs-rec
oset
/nat-set/
max-ifins
wlarray
/
below-rec
wlarray
/
free-ecs
set-basic
/nat-set/
Extension
wlarray
/
in-free-h
Used simplifier rules:
wlentry
/
elim-02
nat
/
lez
wlarray
/
free-ecs-base
wlarray
/
below-base
nat-basic
/
lf
nat-basic
/
lf-02
oelem
/nat-set/
transitivity
nat-basic
/
f
oelem
/nat-set/
ls-le
nat-basic
/
s-04
nat
/
prop-07
nat
/
ls-01
nat-basic
/
c
nat-basic
/
a
nat
/
succ-01
set-basic
/nat-set/
size-zero
set-basic
/nat-set/
size-zero-01
nat
/
lels-02
nat
/
gr-def
nat
/
ls-le-simp
wlarray
/
below-rem-in
set-union
/nat-set/
delete-insert
wlarray
/
below-rem-notin
set-basic
/nat-set/
ne
nat
/
le-ls-simp
nat
/
lels-03
nat-basic
/
lf-01
nat
/
anti
nat
/
lels
set-basic
/nat-set/
In-empty
wlarray
/
in-below
nat
/
le-def
oelem
/nat-set/
irreflexivity
nat
/
ler
wlentry
/
sel-04
wlentry
/
sel-05