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Proof step 109 from proof prepost-init-vols-mappings (previous step)

# wlar0 = # wlar, # apebs = # wlar, apebs[m5] = mkpeb(aehdr1, avidhdr(v0, m1, m9, m10, m11), buf1, m12, false), 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, used), m1 < vtbl[v0], 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-peb(mkpeb(aehdr1, avidhdr(v0, m1, m9, m10, m11), buf1, m12, false)), valid-peb(v0, m1, mkpeb(aehdr1, avidhdr(v0, m1, m9, m10, m11), buf1, m12, false)), 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 ∈ vtbl, v0 × m1 ∈ recs1, q1 ⊆ q + eq-entry(m5, v0 × m1) ', q1 ⊆ q, recs1 ⊥ vols ⊦ m5 = n, recs1 = ∅, valid-eraseq-strong(apebs, vtbl, q + eq-entry(m5, v0 × m1) '), m5 ∈ q, VTBL_VOLID ∈ vols0, VTBL_VOLID × VTBL_LNUM ∈ recs1, VTBL_VOLID ∈ vols, n ∈ q1, v0 ∈ vols ∧ m1 < # vols[v0]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 110:
⊦ valid-wl(apebs, wlar) ↔ (∀ n. n < # wlar → (wlar[n].status = erroneous ↔ apebs[n].bad) ∧ (wlar[n].status = free → apebs[n].vidhdr = empty) ∧ (wlar[n].status ≠ erroneous ∧ wlar[n].status ≠ erasing → apebs[n].echdr = aechdr(wlar[n].ec)) ∧ (wlar[n].status = used → (∃ v, m. valid-peb(v, m, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m, apebs).max)))
Proof step 111:
# apebs = # wlar, # wlar0 = # wlar, wlar[m5] = wl-entry(m7, used), 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), apebs[m5] = mkpeb(aehdr1, avidhdr(v0, m1, m9, m10, m11), buf1, m12, false), m5 < # wlar, m1 < vtbl[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-peb(v0, m1, mkpeb(aehdr1, avidhdr(v0, m1, m9, m10, m11), buf1, m12, false)), valid-peb(mkpeb(aehdr1, avidhdr(v0, m1, m9, m10, m11), buf1, m12, false)), valid-recs(apebs, wlar0, recs0), valid-vtbl(apebs, vols, wlar, n), valid-vtbl(apebs, vols0, wlar0, n), valid-wl(apebs, wlar0), v0 × m1 ∈ recs1, v0 ∈ vtbl, q1 ⊆ q, q1 ⊆ q + eq-entry(m5, v0 × m1) ', recs1 ⊥ vols, ∀ n. n < # wlar → (wlar[n].status = erroneous ↔ apebs[n].bad) ∧ (wlar[n].status = free → apebs[n].vidhdr = empty) ∧ (wlar[n].status ≠ erroneous ∧ wlar[n].status ≠ erasing → apebs[n].echdr = aechdr(wlar[n].ec)) ∧ (wlar[n].status = used → (∃ v, m. valid-peb(v, m, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m, apebs).max)) ⊦ m5 = 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, m5 ∈ q, v0 ∈ vols ∧ m1 < # vols[v0]

Rule argument

spec: ubi-base name: valid-wl seq: ⊦ valid-wl(apebs, wlar) ↔ (∀ n. n < # wlar → (wlar[n].status = erroneous ↔ apebs[n].bad) ∧ (wlar[n].status = free → apebs[n].vidhdr = empty) ∧ ( wlar[n].status ≠ erroneous ∧ wlar[n].status ≠ erasing → apebs[n].echdr = aechdr(wlar[n].ec)) ∧ ( wlar[n].status = used → (∃ v, m. valid-peb(v, m, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m, apebs).max))) subst: [wlar, apebs] → [wlar, apebs] flags: <all paths>

Additional information

Used terms: wlar, apebs