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Proof step 8 from proof valid-wl-free (previous step)

apebs[m] = mkpeb(aehdr, avhdr, buf, m0, stat = erroneous), wlar[m] = wl-entry(m3, stat), m < # wlar, stat = used → valid-peb(v, m2, mkpeb(aehdr, avhdr, buf, m0, stat = erroneous)) ∧ avhdr.sqn = valid-sqns(v, m2, apebs).max, stat ≠ erroneous ∧ stat ≠ erasing → aehdr = aechdr(m3), stat = free → avhdr = empty, ∀ n. n < # wlar → (wlar[m, wl-entry(m1, free)][n].status = erroneous ↔ apebs[n].bad) ∧ (wlar[m, wl-entry(m1, free)][n].status = free → apebs[n].vidhdr = empty) ∧ ( wlar[m, wl-entry(m1, free)][n].status ≠ erroneous ∧ wlar[m, wl-entry(m1, free)][n].status ≠ erasing → apebs[n].echdr = aechdr(wlar[m, wl-entry(m1, free)][n].ec)) ∧ (wlar[m, wl-entry(m1, free)][n].status = used → (∃ v, m. valid-peb(v, m, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m, apebs).max)), ∀ 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)) ⊦ aehdr = aechdr(m1) ∧ avhdr = empty ∧ stat ≠ erroneous

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
wlar[m] = wl-entry(m3, stat), apebs[m] = mkpeb(aehdr, avhdr, buf, m0, stat = erroneous), m < # wlar, stat = free → avhdr = empty, stat ≠ erroneous ∧ stat ≠ erasing → aehdr = aechdr(m3), stat = used → valid-peb(v, m2, mkpeb(aehdr, avhdr, buf, m0, false)) ∧ avhdr.sqn = valid-sqns(v, m2, apebs).max, ∀ 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)), ∀ n. n < # wlar → (wlar[m, wl-entry(m1, free)][n].status = erroneous ↔ apebs[n].bad) ∧ (wlar[m, wl-entry(m1, free)][n].status = free → apebs[n].vidhdr = empty) ∧ ( wlar[m, wl-entry(m1, free)][n].status ≠ erroneous ∧ wlar[m, wl-entry(m1, free)][n].status ≠ erasing → apebs[n].echdr = aechdr(wlar[m, wl-entry(m1, free)][n].ec)) ∧ (wlar[m, wl-entry(m1, free)][n].status = used → (∃ v, m. valid-peb(v, m, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m, apebs).max)) ⊦ aehdr = aechdr(m1) ∧ avhdr = empty ∧ stat ≠ erroneous

Rule argument

Additional information

Used simplifier rules: ⊦ used ≠ erroneous; (s)