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Proof step 25 from proof valid-wl-erasing-update-ec (previous step)

wlar[m] = wl-entry(m0, erasing), apebs[n] = mkpeb(aehdr, avhdr, buf, m2, boolvar), wlar[n] = wl-entry(m4, stat), m < # wlar, n < # 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)) ⊦ n = m, apebs[m].bad, (stat = erroneous ↔ boolvar) ∧ (stat = free → avhdr = empty) ∧ (stat ≠ erroneous ∧ stat ≠ erasing → aehdr = aechdr(m4)) ∧ (stat = used → (∃ v, m1. valid-peb(v, m1, mkpeb(aehdr, avhdr, buf, m2, false)) ∧ avhdr.sqn = valid-sqns(v, m1, apebs).max))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 26:
wlar[n] = wl-entry(m4, stat), apebs[n] = mkpeb(aehdr, avhdr, buf, m2, boolvar), wlar[m] = wl-entry(m0, erasing), apebs[m] = mkpeb(aehdr0, avhdr0, buf0, m3, boolvar0), ¬ boolvar0, 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)) ⊦ n = m, (stat = erroneous ↔ boolvar) ∧ (stat = free → avhdr = empty) ∧ (stat ≠ erroneous ∧ stat ≠ erasing → aehdr = aechdr(m4)) ∧ (stat = used → (∃ v, m1. valid-peb(v, m1, mkpeb(aehdr, avhdr, buf, m2, false)) ∧ avhdr.sqn = valid-sqns(v, m1, apebs).max))

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], aehdr0, avhdr0, buf0, m4, boolvar0]

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], aehdr0, avhdr0, buf0, m4, boolvar0