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Theorem inv-create-volume

ubi-cons(apebs, vols, wlar, q, bflipset, vtblpnum, sqnum), vtblpnum0 = LEB_SIZE, vtblpnum1 = EB_PAGE_SIZE, ubi-io-inv(apebs), apebs0 = apebs, vols0 = vols, q0 = q ⊦ ⟪ubi_create_volume#(v, n, vtblpnum0, vtblpnum1; vols, wlar, q, bflipset, vtblpnum, sqnum, apebs; err)⟫ ( ubi-cons(apebs, vols, wlar, q, bflipset, vtblpnum, sqnum) ∧ ubi-io-inv(apebs) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ id(apebs, apebs0, mapped-pebs(vols)) ∧ (err = ESUCCESS → ¬ v ∈ vols0 ∧ vols = vols0[v, fill(mkebatbl(n), unmapped)] ∧ q.lebrefs ⊆ {VTBL_VOLID × VTBL_LNUM} ) ∧ (err ≠ ESUCCESS → q.lebrefs ⊆ q0.lebrefs ∧ vols = vols0))

Type: A proof obligation
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state: ubi-refine,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 10
Proof steps: 56
Used lemmas: prepost-atomic-leb-change, ubi-io-inv-fwd, lf-valid-wl-not-erroneous, lf-valid-wl-free-emptyvidhdr, lf-valid-vtbl-neq-free, prepost-get-peb, inv-erase-all, create-volume, lf-vtbl-info,
Used spec theorems:
- encoding-vtbl/encode
- store/vtbl/Size-insert
Used simplifier rules:
- set-union/lebrefset/One
- error/disj-78
- error-class/einval
- error/disj-35
- error-class/enospc
- set-basic/lebrefset/sub-idem
- nat/gr-def
- nat-mult/two-02
- nat-mult/rsucc-02
- erasequeue/in-empty
- list-set/erasequeue-base/subset-empty
- set-basic/lebrefset/subset-empty
- ubi-base/idset-refl
- wlentry/elim-02
- apeb/elim
- ubi-io-inv/peb-inv-write-echdr
- ubi-io-inv/peb-inv-empty-vidhdr
- wlstatus/disj-04
- store/vtbl/neq
- store/vtbl/empty
- nat-mult/coef-19
- nat-mult/mult-c
- nat-mult/mult-a
- nat-mult/one
- nat-mult/numeral-21
- nat/fle-01
- nat-basic/f
- nat/le-def
- vtbl-conv/to-vtbl-size
- nat-basic/l
- nat-basic/a
- nat-basic/c
- vtbl-conv/to-vtbl-in
- nat/ge
- array/buffer/Size-mkarray
- eraseblock/lebsize-page-size-is-aligned
- list/erasequeue-base/a
- list/erasequeue-base/Nil
- wlentry/sel-04
- nat/let
- array-splice/buffer/append-a
- array-splice/buffer/mkemparray0-append-right
- nat/zero
- list/erasequeue-base/Last
- array-copy/buffer/subarray-elim
- ubi-base/ubi-cons
- nat/ler
- nat-basic/lf-01
- set-union/nat-set/int-c
- set-union/nat-set/int-a
- set-union/nat-set/int-idem
- array-copy/apebs/idexcept-size
- ubi-base/idset-trans-intersect
- encoding-vtbl/is-encoded-unique
- ubi-base/valid-eraseqd-one
- set-basic/lebrefset/in-04
- set-basic/lebrefset/sub-one-02
- erasequeue/lebrefs-lref
- store/volumes/inj-put
- ubi-base/mapped-pebs-add-empty-vol
- store/volumes/in-neq
- store/volumes/insins
- store/volumes/At-same
- store/volumes/In-insert
- ubi-io-inv/inv-size
- nat/ls-le-simp
- nat/lels
- ubi-base/valid-eraseqd-base
- ubi-base/valid-eraseqp-base
- erasequeue/lebrefs-base
- set-basic/lebrefset/sub-e
- error-class/not-esuccess
- erasequeue/subseteq-lebrefs-subseteq