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Proof step 85 from proof prepost-init-vols-mappings (previous step)

# apebs = # wlar, # wlar0 = # wlar, v × m0 ∈ recs1 ∧ m3 = n0 ∨ v ∈ vols ∧ m0 < # vols[v] ∧ vols[v][m0] = ⌜n0⌝ ↔ wlar[n0].status = used ∧ n0 < # wlar ∧ avhdr0.valid? ∧ avhdr0.vol = v ∧ avhdr0.leb = m0 ∧ n0 ≠ n, wlar[m5] = wl-entry(m7, stat), recs1[v × m0] = recovery-entry(m3, m4), apebs[n] = mkpeb(aehdr, avhdr, buf, m, boolvar), apebs[n0] = mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0), recs1[v0 × m1] = recovery-entry(m5, m6), wlar[m5, wl-entry(m7, erasing)][n0] = wl-entry(m8, stat0), m5 < # wlar, 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), v0 × m1 ∈ recs1, q1 ⊆ q, q1 ⊆ q + eq-entry(m5, v0 × m1) ', recs1 ⊥ vols, ∀ v, m, n0. v × m ∈ recs1 ∧ recs1[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 ⊦ v × m0 ≠ v0 × m1 ∧ v × m0 ∈ recs1 ∧ m3 = n0 ∨ v ∈ vols ∧ m0 < # vols[v] ∧ vols[v][m0] = ⌜n0⌝ ↔ stat0 = used ∧ n0 < # wlar ∧ avhdr0.valid? ∧ avhdr0.vol = v ∧ avhdr0.leb = m0 ∧ n0 ≠ n, recs1 = ∅, n ∈ q1, VTBL_VOLID ∈ vols, VTBL_VOLID × VTBL_LNUM ∈ recs1, VTBL_VOLID ∈ vols0, v0 ∈ vols ∧ m1 < # vols[v0]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 86:
# wlar0 = # wlar, # apebs = # wlar, v × m0 ∈ recs1 ∧ m3 = n0 ∨ v ∈ vols ∧ m0 < # vols[v] ∧ vols[v][m0] = ⌜n0⌝ ↔ stat1 = used ∧ n0 < # wlar ∧ avhdr0.valid? ∧ avhdr0.vol = v ∧ avhdr0.leb = m0 ∧ n0 ≠ n, wlar[m5, wl-entry(m7, erasing)][n0] = wl-entry(m8, stat0), recs1[v0 × m1] = recovery-entry(m5, m6), apebs[n0] = mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0), apebs[n] = mkpeb(aehdr, avhdr, buf, m, boolvar), recs1[v × m0] = recovery-entry(m3, m4), wlar[m5] = wl-entry(m7, stat), wlar[n0] = wl-entry(m9, stat1), m5 < # wlar, 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), v0 × m1 ∈ recs1, q1 ⊆ q + eq-entry(m5, v0 × m1) ', q1 ⊆ q, recs1 ⊥ vols, ∀ v, m, n0. v × m ∈ recs1 ∧ recs1[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 ⊦ v × m0 ≠ v0 × m1 ∧ v × m0 ∈ recs1 ∧ m3 = n0 ∨ v ∈ vols ∧ m0 < # vols[v] ∧ vols[v][m0] = ⌜n0⌝ ↔ stat0 = used ∧ n0 < # wlar ∧ avhdr0.valid? ∧ avhdr0.vol = v ∧ avhdr0.leb = m0 ∧ n0 ≠ n, recs1 = ∅, VTBL_VOLID ∈ vols0, VTBL_VOLID × VTBL_LNUM ∈ recs1, VTBL_VOLID ∈ vols, n ∈ q1, v0 ∈ vols ∧ m1 < # vols[v0]

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], m9, stat1]

Additional information

Used simplifier rules: ⊦ m = wle.ec ∧ stat = wle.status ↔ wle = wl-entry(m, stat); (elim) Used terms: wlar[n0], m9, stat1