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Proof step 2 from proof valid-wl-markbad (previous step)

# apebs = # wlar, m < # apebs, valid-wl(apebs, wlar) ⊦ valid-wl(apebs[m, mkpeb(aehdr, avhdr, buf, m0, true)], wlar[m, wl-entry(m1, erroneous)])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
# apebs = # wlar, n < # wlar, m < # 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)) ⊦ (wlar[m, wl-entry(m1, erroneous)][n].status = erroneous ↔ apebs[m, mkpeb(aehdr, avhdr, buf, m0, true)][n].bad) ∧ (wlar[m, wl-entry(m1, erroneous)][n].status = free → apebs[n].vidhdr = empty) ∧ (wlar[m, wl-entry(m1, erroneous)][n].status ≠ erroneous ∧ wlar[n].status ≠ erasing → apebs[n].echdr = aechdr(wlar[n].ec)) ∧ ( wlar[m, wl-entry(m1, erroneous)][n].status = used → (∃ v, m2. valid-peb(v, m2, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m2, apebs[m, mkpeb(aehdr, avhdr, buf, m0, true)]).max))

Rule argument

Additional information

Used simplifier rules: valid-wl: ⊦ 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)));% ⊦ m < n → n ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ used ≠ erroneous; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)%m ≠ n ⊦ wlar[m, wle][n] = wlar[n]; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).bad ↔ boolvar; (s)% ⊦ m < # apebs → apebs[m, apeb][m] = apeb; (s)%m ≠ n ⊦ apebs[m, apeb][n] = apebs[n]; (s)% ⊦ free ≠ erroneous; (s)% ⊦ wl-entry(m, stat).status = stat; (s)% ⊦ m < # wlar → wlar[m, wle][m] = wle; (s)% ⊦ # wlar[n, wle] = # wlar; (s)