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Proof step 18 from proof valid-wl-free (previous step)

apebs[m] = mkpeb(aechdr(m1), empty, buf, m0, false), apebs[n] = mkpeb(aehdr, avhdr, buf0, m2, boolvar), wlar[n] = wl-entry(m4, stat), m < # wlar, n < # wlar, m < # wlar → (wlar[m].status = erroneous ↔ apebs[m].bad) ∧ (wlar[m].status = free → apebs[m].vidhdr = empty) ∧ (wlar[m].status ≠ erroneous ∧ wlar[m].status ≠ erasing → apebs[m].echdr = aechdr(wlar[m].ec)) ∧ (wlar[m].status = used → (∃ v, m0. valid-peb(v, m0, apebs[m]) ∧ apebs[m].vidhdr.sqn = valid-sqns(v, m0, apebs).max)), ∀ 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, (stat = erroneous ↔ boolvar) ∧ (stat = free → avhdr = empty) ∧ (stat ≠ erroneous ∧ stat ≠ erasing → aehdr = aechdr(m4)) ∧ (stat = used → (∃ v, m3. valid-peb(v, m3, mkpeb(aehdr, avhdr, buf0, m2, false)) ∧ avhdr.sqn = valid-sqns(v, m3, apebs).max))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
apebs[m] = mkpeb(aechdr(m1), empty, buf, m0, false), apebs[n] = mkpeb(aehdr, avhdr, buf0, m2, boolvar), wlar[n] = wl-entry(m4, stat), m < # wlar, n < # wlar, wlar[m].status ≠ erasing → m1 = wlar[m].ec, ∀ 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)) ⊦ wlar[m].status = erroneous, wlar[m].status = used, n = m, (stat = erroneous ↔ boolvar) ∧ (stat = free → avhdr = empty) ∧ (stat ≠ erroneous ∧ stat ≠ erasing → aehdr = aechdr(m4)) ∧ (stat = used → (∃ v, m3. valid-peb(v, m3, mkpeb(aehdr, avhdr, buf0, m2, false)) ∧ avhdr.sqn = valid-sqns(v, m3, apebs).max))

Rule argument

Additional information

Used simplifier rules: ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ aechdr(m) = aechdr(m0) ↔ m = m0; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).echdr = aehdr; (s)% ⊦ ¬ valid-peb(v, m, mkpeb(aehdr, empty, buf, m0, boolvar)); (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).bad ↔ boolvar; (s)