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Proof step 2 from proof valid-wl-erasing-update-ec (previous step)

wlar[m] = wl-entry(m0, erasing), m < # wlar ⊦ valid-wl(apebs, wlar[m, wl-entry(m1, erasing)]) ↔ valid-wl(apebs, wlar)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
wlar[m] = wl-entry(m0, erasing), m < # wlar ⊦ (∀ n. n < # wlar → (wlar[m, wl-entry(m1, erasing)][n].status = erroneous ↔ apebs[n].bad) ∧ (wlar[m, wl-entry(m1, erasing)][n].status = free → apebs[n].vidhdr = empty) ∧ (wlar[n].status ≠ erroneous ∧ wlar[m, wl-entry(m1, erasing)][n].status ≠ erasing → apebs[n].echdr = aechdr(wlar[n].ec)) ∧ (wlar[m, wl-entry(m1, erasing)][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)))

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)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%m ≠ n ⊦ wlar[m, wle][n] = wlar[n]; (s)% ⊦ erroneous ≠ erasing; (s)% ⊦ wl-entry(m, stat).status = stat; (s)% ⊦ m < # wlar → wlar[m, wle][m] = wle; (s)% ⊦ # wlar[n, wle] = # wlar; (s)