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Proof step 8 from proof lf-mapped-valid-peb (previous step)

wlar[n] = wl-entry(m0, used), vols[v][m] = ⌜n⌝ , m < # vols[v], n < # wlar, valid-ebatbl(apebs, wlar, vols, n0), v ∈ vols, 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)) ⊦ n = n0, valid-peb(v, m, apebs[n])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
apebs[n].echdr = aechdr(m0), apebs[n].vidhdr.sqn = valid-sqns(v0, m1, apebs).max, wlar[n] = wl-entry(m0, used), vols[v][m] = ⌜n⌝ , m < # vols[v], n < # wlar, valid-ebatbl(apebs, wlar, vols, n0), valid-peb(v0, m1, apebs[n]), v ∈ vols ⊦ n = n0, apebs[n].bad, v0 = v ∧ m1 = m

Rule argument

Additional information

Used simplifier rules: ⊦ used ≠ free; (s)% ⊦ wl-entry(m, stat).ec = m; (s)% ⊦ used ≠ erasing; (s)%⊦ valid-peb(v0, m0, apeb) → (valid-peb(v1, m1, apeb) ↔ v0 = v1 ∧ m0 = m1); (s)% ⊦ used ≠ erroneous; (s)% ⊦ wl-entry(m, stat).status = stat; (s)