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Proof step 28 from proof inv-format (previous step)

(∅)[default-volid, fill(mkabstractvolume(n), erased)][v][m].mapped?, m < # (∅)[default-volid, fill(mkabstractvolume(n), erased)][v], v ∈ (∅)[default-volid, fill(mkabstractvolume(n), erased)] ⊦ # (∅)[default-volid, fill(mkabstractvolume(n), erased)][v][m].data = LEB_SIZE ∧ (∅)[default-volid, fill(mkabstractvolume(n), erased)][v][m].fill ≤ LEB_SIZE ∧ is-aligned((∅)[default-volid, fill(mkabstractvolume(n), erased)][v][m].fill, EB_PAGE_SIZE) ∧ range= ((∅)[default-volid, fill(mkabstractvolume(n), erased)][v][m].data, (∅)[default-volid, fill(mkabstractvolume(n), erased)][v][m].fill, emptyleb, 0, LEB_SIZE - (∅)[default-volid, fill(mkabstractvolume(n), erased)][v][m].fill)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 29:
(∅)[default-volid, fill(mkabstractvolume(n), erased)][v][m] = mapped(buf, m0), (∅)[default-volid, fill(mkabstractvolume(n), erased)][v][m].mapped?, m < # (∅)[default-volid, fill(mkabstractvolume(n), erased)][v], v ∈ (∅)[default-volid, fill(mkabstractvolume(n), erased)] ⊦ # buf = LEB_SIZE ∧ m0 ≤ LEB_SIZE ∧ is-aligned(m0, EB_PAGE_SIZE) ∧ range=(buf, m0, emptyleb, 0, LEB_SIZE - m0)

Rule argument

spec: leb name: elim seq: ⊦ leb.mapped? → (buf = leb.data ∧ m = leb.fill ↔ leb = mapped(buf, m)) subst: [leb, buf, m] → [(∅)[default-volid, fill(mkabstractvolume(n), erased)][v][m], buf, m0]

Additional information

Used simplifier rules: ⊦ leb.mapped? → (buf = leb.data ∧ m = leb.fill ↔ leb = mapped(buf, m)); (elim) Used terms: (∅)[default-volid, fill(mkabstractvolume(n), erased)][v][m], buf, m0