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Proof step 61 from proof vols-is-max-is-min-eraseq (previous step)

# apebs = # wlar1, # wlar0 = # wlar1, avhdr.leb = VTBL_LNUM, avhdr0.sqn = valid-sqns(VTBL_VOLID, VTBL_LNUM, apebs).max, avhdr.vol = VTBL_VOLID, wlar0[m0] = wl-entry(m3, erasing), apebs[n0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), wlar1[m0] = wl-entry(m5, used), apebs[m0] = mkpeb(aechdr(m5), avhdr0, buf0, m4, false), wlar0[n0] = wl-entry(m6, used), n0 < # wlar1, m0 < # wlar1, bflipset-cons(bflipset0, wlar0), bflipset-cons(bflipset, wlar1), is-encoded(to-vtbl(vols0), buf), is-encoded(to-vtbl(vols1), buf0), unique-sqns(apebs), valid-ebatbl(apebs, wlar0, vols0, n0), valid-eraseq(apebs, q0), valid-eraseq(q0), valid-eraseq(apebs, q1), valid-eraseq(wlar1, q1), valid-eraseq(q1), valid-eraseq-strong(apebs, to-vtbl(vols0), q0), valid-global-sqn(apebs, n1), valid-global-sqn(apebs, m1), valid-peb(VTBL_VOLID, VTBL_LNUM, mkpeb(aechdr(m5), avhdr0, buf0, m4, false)), eq-entry(m0, VTBL_VOLID × VTBL_LNUM) ∈ q0, m0 ∈ q0, ∀ v. (v ∈ vols1 ↔ v ∈ vols0) ∧ (v ∈ vols1 → # vols1[v] = # vols0[v] ∧ (∀ m. m < # vols1[v] ∧ vols1[v][m] ≠ unmapped → vols1[v][m] = vols0[v][m])), ∀ n. n < # wlar0 → (wlar0[n].status = erroneous ↔ apebs[n].bad) ∧ (wlar0[n].status = free → apebs[n].vidhdr = empty) ∧ (wlar0[n].status ≠ erroneous ∧ wlar0[n].status ≠ erasing → apebs[n].echdr = aechdr(wlar0[n].ec)) ∧ (wlar0[n].status = used → (∃ v, m. valid-peb(v, m, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m, apebs).max)) ⊦ avhdr0 = empty, VTBL_VOLID ∈ vols0, VTBL_VOLID ∈ vols1, VTBL_VOLID × VTBL_LNUM ∈ q1

User applied rule all left

And obtained the following new goals

Proof step 62:
# wlar0 = # wlar1, # apebs = # wlar1, avhdr.leb = VTBL_LNUM, avhdr0.sqn = valid-sqns(VTBL_VOLID, VTBL_LNUM, apebs).max, avhdr.vol = VTBL_VOLID, wlar0[n0] = wl-entry(m6, used), apebs[m0] = mkpeb(aechdr(m5), avhdr0, buf0, m4, false), wlar1[m0] = wl-entry(m5, used), apebs[n0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), wlar0[m0] = wl-entry(m3, erasing), m0 < # wlar1, n0 < # wlar1, bflipset-cons(bflipset, wlar1), bflipset-cons(bflipset0, wlar0), is-encoded(to-vtbl(vols1), buf0), is-encoded(to-vtbl(vols0), buf), unique-sqns(apebs), valid-ebatbl(apebs, wlar0, vols0, n0), valid-eraseq(q1), valid-eraseq(wlar1, q1), valid-eraseq(apebs, q1), valid-eraseq(q0), valid-eraseq(apebs, q0), valid-eraseq-strong(apebs, to-vtbl(vols0), q0), valid-global-sqn(apebs, m1), valid-global-sqn(apebs, n1), valid-peb(VTBL_VOLID, VTBL_LNUM, mkpeb(aechdr(m5), avhdr0, buf0, m4, false)), m0 ∈ q0, eq-entry(m0, VTBL_VOLID × VTBL_LNUM) ∈ q0, n0 < # wlar0 → (wlar0[n0].status = erroneous ↔ apebs[n0].bad) ∧ (wlar0[n0].status = free → apebs[n0].vidhdr = empty) ∧ (wlar0[n0].status ≠ erroneous ∧ wlar0[n0].status ≠ erasing → apebs[n0].echdr = aechdr(wlar0[n0].ec)) ∧ (wlar0[n0].status = used → (∃ v, m. valid-peb(v, m, apebs[n0]) ∧ apebs[n0].vidhdr.sqn = valid-sqns(v, m, apebs).max)), ∀ v. (v ∈ vols1 ↔ v ∈ vols0) ∧ (v ∈ vols1 → # vols1[v] = # vols0[v] ∧ (∀ m. m < # vols1[v] ∧ vols1[v][m] ≠ unmapped → vols1[v][m] = vols0[v][m])) ⊦ avhdr0 = empty, VTBL_VOLID × VTBL_LNUM ∈ q1, VTBL_VOLID ∈ vols1, VTBL_VOLID ∈ vols0

Rule argument

pos: left 31 terms: n0 abort: F discard: T computed: T

Additional information

Used terms: n0