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Proof step 17 from proof inv-create-volume (previous step)

avols[v, fill(mkabstractvolume(n), erased)][v0][m].mapped?, m < # avols[v, fill(mkabstractvolume(n), erased)][v0], ebm-cons(avols), v0 ∈ avols[v, fill(mkabstractvolume(n), erased)] ⊦ v ∈ avols, # avols[v, fill(mkabstractvolume(n), erased)][v0][m].data = LEB_SIZE ∧ avols[v, fill(mkabstractvolume(n), erased)][v0][m].fill ≤ LEB_SIZE ∧ is-aligned(avols[v, fill(mkabstractvolume(n), erased)][v0][m].fill, EB_PAGE_SIZE) ∧ range= (avols[v, fill(mkabstractvolume(n), erased)][v0][m].data, avols[v, fill(mkabstractvolume(n), erased)][v0][m].fill, emptyleb, 0, LEB_SIZE - avols[v, fill(mkabstractvolume(n), erased)][v0][m].fill)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 18:
avols[v, fill(mkabstractvolume(n), erased)][v0][m] = mapped(buf, m0), avols[v, fill(mkabstractvolume(n), erased)][v0][m].mapped?, m < # avols[v, fill(mkabstractvolume(n), erased)][v0], ebm-cons(avols), v0 ∈ avols[v, fill(mkabstractvolume(n), erased)] ⊦ v ∈ avols, # 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] → [avols[v, fill(mkabstractvolume(n), erased)][v0][m], buf, m0]

Additional information

Used simplifier rules: ⊦ leb.mapped? → (buf = leb.data ∧ m = leb.fill ↔ leb = mapped(buf, m)); (elim) Used terms: avols[v, fill(mkabstractvolume(n), erased)][v0][m], buf, m0