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Proof step 36 from proof prepost-init-vols-mappings (previous step)

# wlar = # apebs, avhdr0.leb = VTBL_LNUM, avhdr.leb = VTBL_LNUM, avhdr.vol = VTBL_VOLID, avhdr0.vol = VTBL_VOLID, recs0[VTBL_VOLID × VTBL_LNUM] = recovery-entry(n0, m3), apebs[n] = mkpeb(aehdr, avhdr, buf, m, false), apebs[n0] = mkpeb(aehdr0, avhdr0, buf0, m1, false), wlar[n0] = wl-entry(m4, used), wlar[n] = wl-entry(m0, used), avhdr0.valid?, n0 < # apebs, n < # apebs, bflipset-cons(bflipset, wlar), is-encoded(to-vtbl(vols), buf), unique-sqns(apebs), unmapped-vols(vols), valid-eraseq(wlar, q), valid-eraseq-stronger(apebs, q), VTBL_VOLID × VTBL_LNUM ∈ recs0, ∀ n. n < # apebs → (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)) ⊦ n0 = n, VTBL_VOLID ∈ vols, n ∈ q

User applied rule all left

And obtained the following new goals

Proof step 37:
# wlar = # apebs, avhdr.leb = VTBL_LNUM, avhdr0.leb = VTBL_LNUM, avhdr0.vol = VTBL_VOLID, avhdr.vol = VTBL_VOLID, wlar[n] = wl-entry(m0, used), wlar[n0] = wl-entry(m4, used), apebs[n0] = mkpeb(aehdr0, avhdr0, buf0, m1, false), apebs[n] = mkpeb(aehdr, avhdr, buf, m, false), recs0[VTBL_VOLID × VTBL_LNUM] = recovery-entry(n0, m3), avhdr0.valid?, n < # apebs, n0 < # apebs, bflipset-cons(bflipset, wlar), is-encoded(to-vtbl(vols), buf), unique-sqns(apebs), unmapped-vols(vols), valid-eraseq(wlar, q), valid-eraseq-stronger(apebs, q), VTBL_VOLID × VTBL_LNUM ∈ recs0, n0 < # apebs → (wlar[n0].status = erroneous ↔ apebs[n0].bad) ∧ (wlar[n0].status = free → apebs[n0].vidhdr = empty) ∧ (wlar[n0].status ≠ erroneous ∧ wlar[n0].status ≠ erasing → apebs[n0].echdr = aechdr(wlar[n0].ec)) ∧ (wlar[n0].status = used → (∃ v, m. valid-peb(v, m, apebs[n0]) ∧ apebs[n0].vidhdr.sqn = valid-sqns(v, m, apebs).max)), ∀ n. n < # apebs → (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)) ⊦ n0 = n, n ∈ q, VTBL_VOLID ∈ vols

Rule argument

pos: left 21 terms: n0 abort: F discard: F computed: T

Additional information

Used terms: n0