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Proof step 27 from proof valid-wl-next-free (previous step)

# apebs = # wlar, wlar[n] = wl-entry(m4, used), apebs[n] = mkpeb(aechdr(m4), avhdr, buf0, m3, false), apebs[m] = mkpeb(aechdr(m0), empty, buf, m1, false), n < m, m < # wlar, n < # wlar, n + 1 < # 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, m2. valid-peb(v, m2, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m2, apebs, m).max)) ⊦ n = m, ∃ v, m2. valid-peb(v, m2, mkpeb(aechdr(m4), avhdr, buf0, m3, false)) ∧ avhdr.sqn = valid-sqns(v, m2, apebs, m).max

Heuristic quantifier applied rule all left

And closed the goal!

Rule argument

pos: left 9 terms: n

Additional information

Used simplifier rules: ⊦ wl-entry(m, stat).status = stat; (s)% ⊦ used ≠ erroneous; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).bad ↔ boolvar; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ used ≠ erasing; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).echdr = aehdr; (s)% ⊦ wl-entry(m, stat).ec = m; (s)% ⊦ aechdr(m) = aechdr(m0) ↔ m = m0; (s)% ⊦ used ≠ free; (s)%⊦ valid-peb(v0, m0, apeb) → (valid-peb(v1, m1, apeb) ↔ v0 = v1 ∧ m0 = m1); (s) Used terms: n