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Proof step 38 from proof vols-is-max-is-max-vols (previous step)

# 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(aehdr0, avidhdr(v, m, m6, m7, m8), buf0, m9, boolvar0), 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-wl(apebs, wlar1), valid-wl(apebs, wlar0), v ∈ vols1, v ∈ vols0 ⊦ m5 = m0, ⌜m5⌝ = vols0[v][m], VTBL_VOLID ∈ vols1, VTBL_VOLID ∈ vols0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 39:
⊦ 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 40:
# 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, ∀ n. n < # wlar1 → (wlar1[n].status = erroneous ↔ apebs[n].bad) ∧ (wlar1[n].status = free → apebs[n].vidhdr = empty) ∧ (wlar1[n].status ≠ erroneous ∧ wlar1[n].status ≠ erasing → apebs[n].echdr = aechdr(wlar1[n].ec)) ∧ (wlar1[n].status = used → (∃ v, m. valid-peb(v, m, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m, apebs).max)) ⊦ m5 = m0, ⌜m5⌝ = vols0[v][m], VTBL_VOLID ∈ vols0, VTBL_VOLID ∈ vols1

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] → [wlar1, apebs] flags: <all paths>

Additional information

Used terms: wlar1, apebs