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Proof step 5 from proof valid-wl-erasing-invalidate (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
# apebs = # wlar, wlar[m] = wl-entry(m0, erasing), apebs[m, mkpeb(aehdr, avhdr, buf, m2, false)][n] = mkpeb(aehdr0, avhdr0, buf0, m3, boolvar), 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)) ⊦ valid-peb(mkpeb(aehdr, avhdr, buf, m2, false)), (wlar[n].status = erroneous ↔ boolvar) ∧ (wlar[n].status = free → avhdr0 = empty) ∧ (wlar[n].status ≠ erroneous ∧ wlar[n].status ≠ erasing → aehdr0 = aechdr(wlar[n].ec)) ∧ ( wlar[n].status = used → (∃ v, m1. valid-peb(v, m1, apebs[m, mkpeb(aehdr, avhdr, buf, m2, false)][n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m1, apebs[m, mkpeb(aehdr, avhdr, buf, m2, false)]).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, mkpeb(aehdr, avhdr, buf, m2, false)][n], aehdr0, avhdr0, buf0, m3, 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, mkpeb(aehdr, avhdr, buf, m2, false)][n], aehdr0, avhdr0, buf0, m3, boolvar