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Proof step 3 from proof valid-wl-next-invalid-erase (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
# apebs = # wlar, apebs[m] = mkpeb(aehdr, avhdr, buf, m2, boolvar), m < # wlar, ∀ n. n < m → (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, m1. valid-peb(v, m1, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m1, apebs, m).max)) ⊦ (∀ n. ¬ m < n → (wlar[m, wl-entry(m0, erasing)][n].status = erroneous ↔ apebs[n].bad) ∧ (wlar[m, wl-entry(m0, erasing)][n].status = free → apebs[n].vidhdr = empty) ∧ (wlar[n].status ≠ erroneous ∧ wlar[m, wl-entry(m0, erasing)][n].status ≠ erasing → apebs[n].echdr = aechdr(wlar[n].ec)) ∧ ( wlar[m, wl-entry(m0, erasing)][n].status = used → (∃ v, m1. valid-peb(v, m1, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m1, apebs, m).max))) ↔ ¬ boolvar, valid-peb(apebs[m])

Rule argument

spec: apeb name: elim seq: ⊦ ( ( (aehdr = apeb.echdr ∧ avhdr = apeb.vidhdr) ∧ buf = apeb.data) ∧ m = apeb.fill) ∧ (boolvar ↔ apeb.bad) ↔ apeb = mkpeb(aehdr, avhdr, buf, m, boolvar) subst: [apeb, aehdr, avhdr, buf, m, boolvar] → [apebs[m], aehdr, avhdr, buf, m2, boolvar]

Additional information

Used simplifier rules: ⊦ ( ((aehdr = apeb.echdr ∧ avhdr = apeb.vidhdr) ∧ buf = apeb.data) ∧ m = apeb.fill) ∧ (boolvar ↔ apeb.bad) ↔ apeb = mkpeb(aehdr, avhdr, buf, m, boolvar); (elim) Used terms: apebs[m], aehdr, avhdr, buf, m2, boolvar