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Proof step 161 from proof prepost-init-vols-mappings (previous step)

# wlar0 = # wlar, # apebs = # wlar, apebs[n] = mkpeb(aehdr, avhdr, buf, m, boolvar), apebs[n0] = mkpeb(aehdr0, avhdr0, buf0, m1, boolvar0), 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), q1 ⊆ q, ∅ ⊥ vols, ∀ v, m0, n0. v ∈ vols ∧ m0 < # vols[v] ∧ vols[v][m0] = ⌜n0⌝ ↔ wlar[n0].status = used ∧ n0 < # wlar ∧ apebs[n0].vidhdr.valid? ∧ apebs[n0].vidhdr.vol = v ∧ apebs[n0].vidhdr.leb = m0 ∧ n0 ≠ n ⊦ vols[v][m0] = ⌜n0⌝ ∧ v ∈ vols ∧ m0 < # vols[v] ↔ wlar[n0].status = used ∧ n0 < # wlar ∧ avhdr0.valid? ∧ avhdr0.vol = v ∧ avhdr0.leb = m0 ∧ n0 ≠ n, n ∈ q1, VTBL_VOLID ∈ vols0, VTBL_VOLID ∈ vols

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 162:
# apebs = # wlar, # wlar0 = # wlar, apebs[n0] = mkpeb(aehdr0, avhdr0, buf0, m1, boolvar0), apebs[n] = mkpeb(aehdr, avhdr, buf, m, boolvar), wlar[n0] = wl-entry(m2, stat), 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), q1 ⊆ q, ∅ ⊥ vols, ∀ v, m0, n0. v ∈ vols ∧ m0 < # vols[v] ∧ vols[v][m0] = ⌜n0⌝ ↔ wlar[n0].status = used ∧ n0 < # wlar ∧ apebs[n0].vidhdr.valid? ∧ apebs[n0].vidhdr.vol = v ∧ apebs[n0].vidhdr.leb = m0 ∧ n0 ≠ n ⊦ vols[v][m0] = ⌜n0⌝ ∧ v ∈ vols ∧ m0 < # vols[v] ↔ stat = used ∧ n0 < # wlar ∧ avhdr0.valid? ∧ avhdr0.vol = v ∧ avhdr0.leb = m0 ∧ n0 ≠ n, VTBL_VOLID ∈ vols, VTBL_VOLID ∈ vols0, n ∈ q1

Rule argument

spec: wlentry name: elim-02 seq: ⊦ m = wle.ec ∧ stat = wle.status ↔ wle = wl-entry(m, stat) subst: [wle, m, stat] → [wlar[n0], m2, stat]

Additional information

Used simplifier rules: ⊦ m = wle.ec ∧ stat = wle.status ↔ wle = wl-entry(m, stat); (elim) Used terms: wlar[n0], m2, stat