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Proof step 57 from proof recovery (previous step)

# avols0[v] = # vols0[v], # apebs0 = # wlar0, # wlar = # wlar0, # vols[v] = # vols0[v], apebs0[n] = mkpeb(aehdr, avhdr, avols0[v][m].data, m0, false), vols0[v][m] = ⌜n⌝ , vols[v][m] = ⌜n⌝ , avols0[v][m].mapped?, avhdr.valid?, m < # vols0[v], n < # wlar0, bflipset-cons(bflipset, wlar), bflipset-cons(bflipset0, wlar0), ebm-cons(avols0), is-max(apebs0, vols0, wlar0, q0, bflipset0, vtblpnum3, sqnum), ubi-io-inv(apebs0), ubi-io-peb-inv(mkpeb(aehdr, avhdr, avols0[v][m].data, m0, false)), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar, vols, vtblpnum), valid-ebatbl(apebs0, wlar0, vols0, vtblpnum3), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs0, q), valid-eraseq(q0), valid-eraseq(wlar0, q0), valid-eraseq(apebs0, q0), valid-global-sqn(apebs0, vtblpnum0), valid-global-sqn(apebs0, sqnum), valid-vtbl(apebs0, vols, wlar, vtblpnum), valid-vtbl(apebs0, vols0, wlar0, vtblpnum3), valid-wl(apebs0, wlar), valid-wl(apebs0, wlar0), v ∈ vols0, v ∈ vols, v ∈ avols0, m0 ≤ avols0[v][m].fill, q0.lebrefs ⊆ q.lebrefs, vols0⌈vols, q⌉, avols0[v][m] = erased → ¬ v × m ∈ q ⊦ avols0[v][m] = unmapped, mapped(avols0[v][m].data, avols0[v][m].fill) = avols0[v][m], VTBL_VOLID ∈ vols0, VTBL_VOLID ∈ vols

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: leb name: elim seq: ⊦ leb.mapped? → (buf = leb.data ∧ m = leb.fill ↔ leb = mapped(buf, m)) subst: [leb, buf, m] → [avols0[v][m], buf, m1]

Additional information

Used simplifier rules: ⊦ leb.mapped? → (buf = leb.data ∧ m = leb.fill ↔ leb = mapped(buf, m)); (elim) Used terms: avols0[v][m], buf, m1