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Proof step 25 from proof valid-wl-next-valid-use (previous step)

# apebs = # wlar, wlar[n0] = wl-entry(m3, stat), apebs[n0] = mkpeb(aehdr0, avhdr0, buf0, m0, boolvar0), apebs[m] = mkpeb(aehdr, avhdr, buf, m2, boolvar), valid-sqns(v, n, apebs, m) = ∅, n0 < m, m < # wlar, n0 < # wlar, n0 + 1 < # wlar, valid-peb(v, n, mkpeb(aehdr, avhdr, buf, m2, boolvar)), n0 < m → (wlar[n0].status = erroneous ↔ apebs[n0].bad) ∧ (wlar[n0].status = free → apebs[n0].vidhdr = empty) ∧ (wlar[n0].status ≠ erroneous ∧ wlar[n0].status ≠ erasing → apebs[n0].echdr = aechdr(wlar[n0].ec)) ∧ (wlar[n0].status = used → (∃ v0, m1. valid-peb(v0, m1, apebs[n0]) ∧ apebs[n0].vidhdr.sqn = valid-sqns(v0, m1, apebs, m).max)) ⊦ n0 = m, (stat = erroneous ↔ boolvar0) ∧ (stat = free → avhdr0 = empty) ∧ (stat ≠ erroneous ∧ stat ≠ erasing → aehdr0 = aechdr(m3)) ∧ ( stat = used → (∃ v0, m1. valid-peb(v0, m1, mkpeb(aehdr0, avhdr0, buf0, m0, false)) ∧ avhdr0.sqn = (valid-sqns(v0, m1, apebs, m) ∪ (v = v0 ∧ n = m1 ⊃ {avhdr.sqn} ;∅)).max))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 26:
# apebs = # wlar, avhdr0.sqn = valid-sqns(v0, m1, apebs, m).max, apebs[n0] = mkpeb(aechdr(m3), avhdr0, buf0, m0, false), wlar[n0] = wl-entry(m3, used), apebs[m] = mkpeb(aehdr, avhdr, buf, m2, boolvar), valid-sqns(v, n, apebs, m) = ∅, n0 + 1 < # wlar, n0 < # wlar, m < # wlar, n0 < m, valid-peb(v, n, mkpeb(aehdr, avhdr, buf, m2, boolvar)), valid-peb(v0, m1, mkpeb(aechdr(m3), avhdr0, buf0, m0, false)) ⊦ avhdr0.sqn = (valid-sqns(v0, m1, apebs, m) ∪ (v = v0 ∧ n = m1 ⊃ {avhdr.sqn} ;∅)).max, n0 = m

Rule argument

Additional information

Used simplifier rules: ⊦ used ≠ erasing; (s)%⊦ valid-peb(v0, m0, apeb) → (valid-peb(v1, m1, apeb) ↔ v0 = v1 ∧ m0 = m1); (s)% ⊦ used ≠ free; (s)% ⊦ used ≠ erroneous; (s)% ⊦ wl-entry(m, stat).ec = m; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).echdr = aehdr; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).bad ↔ boolvar; (s)% ⊦ wl-entry(m, stat).status = stat; (s)