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Proof step 10 from proof valid-wl-ebatbl-used-imp-mapped (previous step)

# wlar = # apebs, avhdr.sqn = valid-sqns(v, m, apebs).max, vols[v][# wlar] = ⌜n⌝ ∧ v ∈ vols ∧ # wlar < # vols[v] ↔ wlar[n].status = used ∧ n < # apebs ∧ apebs[n].vidhdr.valid? ∧ apebs[n].vidhdr.vol = v ∧ apebs[n].vidhdr.leb = # wlar ∧ n ≠ n0, apebs[n] = mkpeb(aechdr(m1), avhdr, buf, m0, false), wlar[n] = wl-entry(m1, used), n < # apebs, valid-peb(v, m, mkpeb(aechdr(m1), avhdr, buf, m0, false)), ∀ v, m, n1. vols[v][m] = ⌜n1⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n1].status = used ∧ n1 < # apebs ∧ apebs[n1].vidhdr.valid? ∧ apebs[n1].vidhdr.vol = v ∧ apebs[n1].vidhdr.leb = m ∧ n1 ≠ n0, ∀ 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, v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n⌝

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
# wlar = # apebs, avhdr.sqn = valid-sqns(v, m, apebs).max, vols[v][# apebs] = ⌜n⌝ ∧ v ∈ vols ∧ # apebs < # vols[v] ↔ avhdr.valid? ∧ m = # apebs, apebs[n] = mkpeb(aechdr(m1), avhdr, buf, m0, false), wlar[n] = wl-entry(m1, used), n < # apebs, valid-peb(v, m, mkpeb(aechdr(m1), avhdr, buf, m0, false)), ∀ v, m, n1. vols[v][m] = ⌜n1⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n1].status = used ∧ n1 < # apebs ∧ apebs[n1].vidhdr.valid? ∧ apebs[n1].vidhdr.vol = v ∧ apebs[n1].vidhdr.leb = m ∧ n1 ≠ n0, ∀ 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, v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n⌝

Rule argument

Additional information

Used simplifier rules: ⊦ valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)) → avhdr.leb = m; (s)%⊦ valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)) → avhdr.vol = v; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ wl-entry(m, stat).status = stat; (s)