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Proof step 4 from proof valid-wl-next-free (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
# apebs = # wlar, apebs[m] = mkpeb(aechdr(m0), empty, buf, m1, false), apebs[n] = mkpeb(aehdr, avhdr, 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, m2. valid-peb(v, m2, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m2, apebs, m).max)) ⊦ (wlar[m, wl-entry(m0, free)][n].status = erroneous ↔ boolvar) ∧ (wlar[m, wl-entry(m0, free)][n].status = free → avhdr = empty) ∧ ( wlar[m, wl-entry(m0, free)][n].status ≠ erroneous ∧ wlar[m, wl-entry(m0, free)][n].status ≠ erasing → aehdr = aechdr(wlar[m, wl-entry(m0, free)][n].ec)) ∧ ( wlar[m, wl-entry(m0, free)][n].status = used → (∃ v, m2. valid-peb(v, m2, mkpeb(aehdr, avhdr, buf0, m3, wlar[n].status = erroneous)) ∧ avhdr.sqn = valid-sqns(v, m2, apebs, m).max))

Rule argument

Additional information

Used simplifier rules: m ≠ n ⊦ wlar[m, wle][n] = wlar[n]; (s)% ⊦ used ≠ free; (s)% ⊦ wl-entry(m, stat).status = stat; (s)% ⊦ m < # wlar → wlar[m, wle][m] = wle; (s)