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Proof step 11 from proof valid-wl-erasing-invalidate0 (previous step)

# apebs = # wlar, wlar[m, wl-entry(m0, erasing)][n] = wl-entry(m6, stat0), apebs[m, mkpeb(aehdr, avhdr, buf, m2, false)][n] = mkpeb(aehdr1, avhdr1, buf1, m4, boolvar0), apebs[n] = mkpeb(aehdr0, avhdr0, buf0, m3, boolvar), wlar[n] = wl-entry(m5, stat), 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, valid-peb(mkpeb(aehdr, avhdr, buf, m2, false)), (stat0 = erroneous ↔ boolvar0) ∧ (stat0 = free → avhdr0 = empty) ∧ (stat ≠ erroneous ∧ stat0 ≠ erasing → aehdr0 = aechdr(m5)) ∧ ( stat0 = used → (∃ v, m1. valid-peb(v, m1, mkpeb(aehdr0, avhdr0, buf0, m3, boolvar)) ∧ avhdr0.sqn = valid-sqns(v, m1, apebs[m, mkpeb(aehdr, avhdr, buf, m2, false)]).max))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
# apebs = # wlar, apebs[n] = mkpeb(aehdr0, avhdr0, buf0, m3, boolvar), wlar[n] = wl-entry(m5, 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, valid-peb(mkpeb(aehdr, avhdr, buf, m2, false)), (stat = erroneous ↔ boolvar) ∧ (stat = free → avhdr0 = empty) ∧ (stat ≠ erroneous ∧ stat ≠ erasing → aehdr0 = aechdr(m5)) ∧ ( stat = used → (∃ v, m0. valid-peb(v, m0, mkpeb(aehdr0, avhdr0, buf0, m3, false)) ∧ avhdr0.sqn = valid-sqns(v, m0, apebs[m, mkpeb(aehdr, avhdr, buf, m2, false)]).max))

Rule argument

Additional information

Used simplifier rules: ⊦ used ≠ erroneous; (s)% ⊦ wl-entry(m, stat) = wl-entry(m0, stat0) ↔ m = m0 ∧ stat = stat0; (ws)%⊦ mkpeb(aehdr, avhdr, buf, m, boolvar) = mkpeb(aehdr0, avhdr0, buf0, m0, boolvar0) ↔ aehdr = aehdr0 ∧ avhdr = avhdr0 ∧ buf = buf0 ∧ m = m0 ∧ (boolvar ↔ boolvar0); (s)% ⊦ m ≠ n → wlar[n, wle][m] = wlar[m]; (s)% ⊦ m ≠ n → apebs[n, apeb][m] = apebs[m]; (s)