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Proof step 61 from proof prepost-init-vols-mappings (previous step)

# wlar0 = # wlar, # apebs = # wlar, v × m0 ∈ recs1 ∧ m3 = n0 ∨ v ∈ vols ∧ m0 < # vols[v] ∧ vols[v][m0] = ⌜n0⌝ ↔ stat = used ∧ n0 < # wlar ∧ avhdr0.valid? ∧ avhdr0.vol = v ∧ avhdr0.leb = m0 ∧ n0 ≠ n, 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[n0] = wl-entry(m7, stat), v = v0, m1 < # vols[v0], 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, v0 ∈ vols, q1 ⊆ q, recs1 ⊥ vols ⊦ v × m0 ≠ v0 × m1 ∧ v × m0 ∈ recs1 ∧ m3 = n0 ∨ v ∈ vols[v0, vols[v0][m1, ⌜m5⌝ ]] ∧ m0 < # vols[v0, vols[v0][m1, ⌜m5⌝ ]][v] ∧ vols[v0, vols[v0][m1, ⌜m5⌝ ]][v][m0] = ⌜n0⌝ ↔ v × m0 ∈ recs1 ∧ m3 = n0 ∨ v ∈ vols ∧ m0 < # vols[v] ∧ vols[v][m0] = ⌜n0⌝ , recs1 = ∅, VTBL_VOLID ∈ vols0, VTBL_VOLID × VTBL_LNUM ∈ recs1, VTBL_VOLID ∈ vols, n ∈ q1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 62:
# apebs = # wlar, # wlar0 = # wlar, v0 × m0 ∈ recs1 ∧ m3 = n0 ∨ m0 < # vols[v0] ∧ vols[v0][m0] = ⌜n0⌝ ↔ stat = used ∧ n0 < # wlar ∧ avhdr0.valid? ∧ avhdr0.vol = v0 ∧ avhdr0.leb = m0 ∧ n0 ≠ n, wlar[n0] = wl-entry(m7, stat), recs1[v0 × 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), m1 < # vols[v0], 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 ∈ vols, v0 × m1 ∈ recs1, q1 ⊆ q, recs1 ⊥ vols ⊦ v0 × m0 ≠ v0 × m1 ∧ v0 × m0 ∈ recs1 ∧ m3 = n0 ∨ m0 < # vols[v0] ∧ vols[v0][m1, ⌜m5⌝ ][m0] = ⌜n0⌝ ↔ v0 × m0 ∈ recs1 ∧ m3 = n0 ∨ m0 < # vols[v0] ∧ vols[v0][m0] = ⌜n0⌝ , recs1 = ∅, n ∈ q1, VTBL_VOLID ∈ vols, VTBL_VOLID × VTBL_LNUM ∈ recs1, VTBL_VOLID ∈ vols0

Rule argument

Additional information

Used simplifier rules: ⊦ # ebatbl[n, ebae] = # ebatbl; (s)% ⊦ vols[v, ebatbl][v] = ebatbl; (s)% ⊦ v ∈ vols[v, ebatbl]; (s)