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Proof step 42 from proof vols-is-max-is-max-vols (previous step)

# vols0[v] = # vols1[v], # apebs = # wlar1, # wlar0 = # wlar1, avhdr.leb = VTBL_LNUM, avhdr.vol = VTBL_VOLID, wlar0[m0] = wl-entry(m3, used), apebs[m0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), wlar1[m0] = wl-entry(m4, used), apebs[m5] = mkpeb(aehdr0, avidhdr(v, m, m6, m7, m8), buf0, m9, boolvar0), wlar1[m5] = wl-entry(m10, used), ⌜m5⌝ = vols1[v][m], m0 < # wlar1, m < # vols1[v], m5 < # wlar1, bflipset-cons(bflipset0, wlar0), bflipset-cons(bflipset1, wlar1), is-encoded(to-vtbl(vols1), buf), unique-sqns(apebs), valid-ebatbl(apebs, wlar0, vols0, m0), valid-eraseq(apebs, q0), valid-eraseq(wlar0, q0), valid-eraseq(q0), valid-eraseq(apebs, q1), valid-eraseq(wlar1, q1), valid-eraseq(q1), valid-eraseq-strong(apebs, to-vtbl(vols1), q0), valid-global-sqn(apebs, n1), valid-global-sqn(apebs, m1), valid-wl(apebs, wlar0), v ∈ vols0, v ∈ vols1, m5 < # wlar1 → (wlar1[m5].status = erroneous ↔ apebs[m5].bad) ∧ (wlar1[m5].status = free → apebs[m5].vidhdr = empty) ∧ (wlar1[m5].status ≠ erroneous ∧ wlar1[m5].status ≠ erasing → apebs[m5].echdr = aechdr(wlar1[m5].ec)) ∧ (wlar1[m5].status = used → (∃ v, m. valid-peb(v, m, apebs[m5]) ∧ apebs[m5].vidhdr.sqn = valid-sqns(v, m, apebs).max)) ⊦ m5 = m0, ⌜m5⌝ = vols0[v][m], VTBL_VOLID ∈ vols0, VTBL_VOLID ∈ vols1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 43:
# wlar0 = # wlar1, # apebs = # wlar1, # vols0[v] = # vols1[v], avhdr.leb = VTBL_LNUM, avhdr.vol = VTBL_VOLID, wlar1[m5] = wl-entry(m10, used), apebs[m5] = mkpeb(aechdr(m10), avidhdr(v, m, valid-sqns(v0, m11, apebs).max, m7, m8), buf0, m9, false), wlar1[m0] = wl-entry(m4, used), apebs[m0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), wlar0[m0] = wl-entry(m3, used), ⌜m5⌝ = vols1[v][m], m5 < # wlar1, m < # vols1[v], m0 < # wlar1, bflipset-cons(bflipset1, wlar1), bflipset-cons(bflipset0, wlar0), is-encoded(to-vtbl(vols1), buf), unique-sqns(apebs), valid-ebatbl(apebs, wlar0, vols0, m0), valid-eraseq(q1), valid-eraseq(wlar1, q1), valid-eraseq(apebs, q1), valid-eraseq(q0), valid-eraseq(wlar0, q0), valid-eraseq(apebs, q0), valid-eraseq-strong(apebs, to-vtbl(vols1), q0), valid-global-sqn(apebs, m1), valid-global-sqn(apebs, n1), valid-peb(v0, m11, mkpeb(aechdr(m10), avidhdr(v, m, valid-sqns(v0, m11, apebs).max, m7, m8), buf0, m9, false)), valid-wl(apebs, wlar0), v ∈ vols1, v ∈ vols0 ⊦ m5 = m0, ⌜m5⌝ = vols0[v][m], VTBL_VOLID ∈ vols1, VTBL_VOLID ∈ vols0

Rule argument

Additional information

Used simplifier rules: ⊦ used ≠ free; (s)% ⊦ wl-entry(m, stat).ec = m; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).echdr = aehdr; (s)% ⊦ used ≠ erasing; (s)% ⊦ avidhdr(v, m, m0, m1, m2).sqn = m0; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).bad ↔ boolvar; (s)% ⊦ used ≠ erroneous; (s)% ⊦ wl-entry(m, stat).status = stat; (s)