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Proof step 15 from proof valid-wl-next-bad (previous step)

# apebs = # wlar, wlar[m, wl-entry(m0, erroneous)][n] = wl-entry(m5, stat0), wlar[n] = wl-entry(m4, stat), apebs[m] = mkpeb(aehdr, avhdr, buf, m2, true), apebs[n] = mkpeb(aehdr0, avhdr0, buf0, m3, boolvar), n < # wlar, m < # wlar, n ≤ m, ∀ 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, (stat0 = erroneous ↔ boolvar) ∧ (stat0 = free → avhdr0 = empty) ∧ (stat0 ≠ erroneous ∧ stat ≠ erasing → aehdr0 = aechdr(m4)) ∧ (stat0 = used → (∃ v, m1. valid-peb(v, m1, mkpeb(aehdr0, avhdr0, buf0, m3, stat = erroneous)) ∧ avhdr0.sqn = valid-sqns(v, m1, apebs, m).max))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
# apebs = # wlar, wlar[n] = wl-entry(m4, stat), apebs[n] = mkpeb(aehdr0, avhdr0, buf0, m3, boolvar), apebs[m] = mkpeb(aehdr, avhdr, buf, m2, true), n + 1 < # wlar, m < # wlar, n < # wlar, n < m, ∀ 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, (stat = erroneous ↔ boolvar) ∧ (stat = free → avhdr0 = empty) ∧ (stat ≠ erroneous ∧ stat ≠ erasing → aehdr0 = aechdr(m4)) ∧ (stat = used → (∃ v, m0. valid-peb(v, m0, mkpeb(aehdr0, avhdr0, buf0, m3, false)) ∧ avhdr0.sqn = valid-sqns(v, m0, apebs, m).max))

Rule argument

Additional information

Used simplifier rules: ⊦ used ≠ erroneous; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m +1 = m + 1; (s)% ⊦ m < n → n ≠ 0; (s)% ⊦ wl-entry(m, stat) = wl-entry(m0, stat0) ↔ m = m0 ∧ stat = stat0; (ws)%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)% ⊦ m ≠ n → wlar[n, wle][m] = wlar[m]; (s)