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Proof step 12 from proof valid-wl-use (previous step)

# apebs = # wlar, apebs[n, mkpeb(aehdr, avhdr, buf, m0, boolvar)][n0] = mkpeb(aehdr0, avhdr0, buf0, m1, boolvar0), apebs[n0] = mkpeb(aehdr1, avhdr1, buf1, m2, boolvar1), wlar[n, wl-entry(aehdr.ec, used)][n0] = wl-entry(m3, stat), n0 = n, n0 < # wlar, n < # wlar, valid-peb(mkpeb(aehdr, avhdr, buf, m0, boolvar)), valid-sqns(avhdr.vol, avhdr.leb, apebs) ≠ ∅ → valid-sqns(avhdr.vol, avhdr.leb, apebs).max < avhdr.sqn, ∀ 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)), ∀ m. m < # wlar ∧ m ≠ n ∧ wlar[m].status = used → apebs[m].vidhdr.vol ≠ avhdr.vol ∨ apebs[m].vidhdr.leb ≠ avhdr.leb ⊦ (stat = erroneous ↔ boolvar0) ∧ (stat = free → avhdr1 = empty) ∧ (stat ≠ erroneous ∧ stat ≠ erasing → aehdr0 = aechdr(m3)) ∧ ( stat = used → (∃ v, m. valid-peb(v, m, mkpeb(aehdr0, avhdr0, buf0, m1, false)) ∧ avhdr0.sqn = valid-sqns(v, m, apebs[n, mkpeb(aehdr, avhdr, buf, m0, boolvar)]).max))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
# apebs = # wlar, apebs[n] = mkpeb(aehdr1, avhdr1, buf1, m2, boolvar1), n < # wlar, valid-peb(mkpeb(aehdr0, avhdr0, buf0, m1, false)), valid-sqns(avhdr0.vol, avhdr0.leb, apebs) ≠ ∅ → valid-sqns(avhdr0.vol, avhdr0.leb, apebs).max < avhdr0.sqn, ∀ m. m < # wlar ∧ m ≠ n ∧ wlar[m].status = used → apebs[m].vidhdr.vol ≠ avhdr0.vol ∨ apebs[m].vidhdr.leb ≠ avhdr0.leb, ∀ 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)) ⊦ (∃ v, m. valid-peb(v, m, mkpeb(aehdr0, avhdr0, buf0, m1, false)) ∧ avhdr0.sqn = valid-sqns(v, m, apebs[n, mkpeb(aehdr0, avhdr0, buf0, m1, false)]).max) ∧ aehdr0 = aechdr(aehdr0.ec)

Rule argument

Additional information

Used simplifier rules: ⊦ valid-peb(mkpeb(aehdr, avhdr, buf, m, true)) ↔ false; (s)% ⊦ used ≠ erasing; (s)% ⊦ used ≠ free; (s)% ⊦ used ≠ erroneous; (s)%⊦ mkpeb(aehdr, avhdr, buf, m, boolvar) = mkpeb(aehdr0, avhdr0, buf0, m0, boolvar0) ↔ aehdr = aehdr0 ∧ avhdr = avhdr0 ∧ buf = buf0 ∧ m = m0 ∧ (boolvar ↔ boolvar0); (s)%m < # apebs ⊦ apebs[m, apeb][m] = apeb; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ wl-entry(m, stat) = wl-entry(m0, stat0) ↔ m = m0 ∧ stat = stat0; (ws)% ⊦ m < # wlar → wlar[m, wle][m] = wle; (s)