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Theorem inv-erase-all

ubi-cons(apebs, vols, wlar, q, bflipset, vtblpnum, sqnum), ubi-io-inv(apebs), apebs0 = apebs, q0 = q ⊦ ⟪ubi_erase_all#(vols, bflipset, vtblpnum, sqnum; wlar, q, apebs; err)⟫ ( ubi-cons(apebs, vols, wlar, q, bflipset, vtblpnum, sqnum) ∧ ubi-io-inv(apebs) ∧ id(apebs, apebs0, mapped-pebs(vols)) ∧ q ⊆ q0 ∧ (err = ESUCCESS → q = []) ∧ (err = ESUCCESS ∨ ⌊err⌋ ))

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 2
Proof steps: 18
Used lemmas: prepost-erase-worker-helper, erase-all, lf-vtbl-info,
Used spec theorems:
- Used simplifier rules:
  - ubi-base/idset-refl
  - list-set/erasequeue-base/subset-ref
  - list-data/erasequeue-base/elim-list-c
  - nat-basic/c
  - nat-basic/a
  - nat-basic/s-04
  - nat-basic/succ
  - list/erasequeue-base/len-05
  - erasequeue/in-concat
  - list/erasequeue-base/c
  - erasequeueentry/elim
  - erasequeue/in-prepend-other
  - erasequeue/in-single
  - nat/lels
  - ubi-base/valid-eraseqw-size-left
  - nat-basic/f
  - ubi-base/ubi-cons
  - list/erasequeue-base/Nil
  - nat-basic/lf-01
  - set-union/nat-set/int-c
  - set-union/nat-set/int-a
  - set-union/nat-set/int-idem
  - array-copy/wlarray-base/idexcept-size
  - array-copy/apebs/idexcept-size
  - ubi-base/idset-trans-intersect
  - list/erasequeue-base/app-02
  - list/erasequeue-base/e
  - list/erasequeue-base/e-01
  - list/erasequeue-base/c-07
  - oelem/nat-set/irreflexivity
  - error-class/not-esuccess
  - list-set/erasequeue-base/subset-rec
  - list/erasequeue-base/a
  - nat-basic/zero-01