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Proof step 145 from proof prepost-init-vols-mappings (previous step)

# wlar0 = # wlar, # apebs = # wlar, apebs[n] = mkpeb(aehdr, avhdr, buf, m, boolvar), bflipset-cons(bflipset0, wlar0), bflipset-cons(bflipset, wlar), is-encoded(vtbl, buf), unique-sqns(apebs), unmapped-vols(vols0), valid-eraseq(wlar0, q1), valid-eraseq(wlar, q), valid-eraseq-strong(apebs, vtbl, q), valid-eraseq-stronger(apebs, q1), valid-recs(apebs, wlar0, recs0), valid-vtbl(apebs, vols0, wlar0, n), valid-vtbl(apebs, vols, wlar, n), valid-wl(apebs, wlar0), valid-wl(apebs, wlar), ladr ∈ recs, # wlar ≤ recs[ladr].pnum, q1 ⊆ q, recs ⊥ vols, ∀ v, m, n0. v × m ∈ recs ∧ recs[v × m].pnum = n0 ∨ v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n0⌝ ↔ wlar[n0].status = used ∧ n0 < # wlar ∧ apebs[n0].vidhdr.valid? ∧ apebs[n0].vidhdr.vol = v ∧ apebs[n0].vidhdr.leb = m ∧ n0 ≠ n ⊦ recs = ∅, n ∈ q1, VTBL_VOLID ∈ vols0, VTBL_VOLID × VTBL_LNUM ∈ recs, VTBL_VOLID ∈ vols, ladr.vol ∈ vols ∧ ladr.leb < # vols[ladr.vol]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 146:
# apebs = # wlar, # wlar0 = # wlar, apebs[n] = mkpeb(aehdr, avhdr, buf, m, boolvar), ladr = v0 × m0, bflipset-cons(bflipset, wlar), bflipset-cons(bflipset0, wlar0), is-encoded(vtbl, buf), unique-sqns(apebs), unmapped-vols(vols0), valid-eraseq(wlar, q), valid-eraseq(wlar0, q1), valid-eraseq-strong(apebs, vtbl, q), valid-eraseq-stronger(apebs, q1), valid-recs(apebs, wlar0, recs0), valid-vtbl(apebs, vols, wlar, n), valid-vtbl(apebs, vols0, wlar0, n), valid-wl(apebs, wlar), valid-wl(apebs, wlar0), ladr ∈ recs, # wlar ≤ recs[ladr].pnum, q1 ⊆ q, recs ⊥ vols, ∀ v, m, n0. v × m ∈ recs ∧ recs[v × m].pnum = n0 ∨ v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n0⌝ ↔ wlar[n0].status = used ∧ n0 < # wlar ∧ apebs[n0].vidhdr.valid? ∧ apebs[n0].vidhdr.vol = v ∧ apebs[n0].vidhdr.leb = m ∧ n0 ≠ n ⊦ recs = ∅, VTBL_VOLID ∈ vols, VTBL_VOLID × VTBL_LNUM ∈ recs, VTBL_VOLID ∈ vols0, n ∈ q1, v0 ∈ vols ∧ m0 < # vols[v0]

Rule argument

spec: lebadress name: elim seq: ⊦ v = ladr.vol ∧ m = ladr.leb ↔ ladr = v × m subst: [ladr, v, m] → [ladr, v0, m0]

Additional information

Used simplifier rules: ⊦ v = ladr.vol ∧ m = ladr.leb ↔ ladr = v × m; (elim) Used terms: ladr, v0, m0