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Proof step 103 from proof prepost-init-vols-mappings (previous step)

# apebs = # wlar, # wlar0 = # wlar, 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 ⊦ recs1 = ∅, valid-eraseq-strong(apebs, vtbl, q + eq-entry(m5, v0 × m1) '), n ∈ q1, VTBL_VOLID ∈ vols, VTBL_VOLID × VTBL_LNUM ∈ recs1, VTBL_VOLID ∈ vols0, v0 ∈ vols ∧ m1 < # vols[v0], (¬ v0 ∈ vtbl ∨ ¬ m1 < vtbl[v0]) ∧ valid-peb(v0, m1, apebs[m5]) ∧ ¬ m5 ∈ q

User applied rule all left

And obtained the following new goals

Proof step 104:
# wlar0 = # wlar, # apebs = # wlar, v0 × m1 ∈ recs1 ∧ recs1[v0 × m1].pnum = m5 ∨ v0 ∈ vols ∧ m1 < # vols[v0] ∧ vols[v0][m1] = ⌜m5⌝ ↔ wlar[m5].status = used ∧ m5 < # wlar ∧ apebs[m5].vidhdr.valid? ∧ apebs[m5].vidhdr.vol = v0 ∧ apebs[m5].vidhdr.leb = m1 ∧ m5 ≠ 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), 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 ⊦ recs1 = ∅, valid-eraseq-strong(apebs, vtbl, q + eq-entry(m5, v0 × m1) '), VTBL_VOLID ∈ vols0, VTBL_VOLID × VTBL_LNUM ∈ recs1, VTBL_VOLID ∈ vols, n ∈ q1, (¬ v0 ∈ vtbl ∨ ¬ m1 < vtbl[v0]) ∧ valid-peb(v0, m1, apebs[m5]) ∧ ¬ m5 ∈ q, v0 ∈ vols ∧ m1 < # vols[v0]

Rule argument

pos: left 28 terms: v0, m1, m5 abort: F discard: T computed: F

Additional information

Used terms: v0, m1, m5