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Proof step 10 from proof valid-wl-next-valid-erase (previous step)

# apebs = # wlar, wlar[m, wl-entry(m0, erasing)][n0] = wl-entry(m5, stat0), apebs[n0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), apebs[m] = mkpeb(aehdr0, avhdr0, buf0, m3, boolvar0), wlar[n0] = wl-entry(m4, stat), m < # wlar, n0 < # wlar, valid-peb(v, n, mkpeb(aehdr0, avhdr0, buf0, m3, boolvar0)), n0 ≤ m, valid-sqns(v, n, apebs, m) ≠ ∅ → avhdr0.sqn < valid-sqns(v, n, apebs, m).max, ∀ n0. 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, (stat0 = erroneous ↔ boolvar) ∧ (stat0 = free → avhdr = empty) ∧ (stat ≠ erroneous ∧ stat0 ≠ erasing → aehdr = aechdr(m4)) ∧ ( stat0 = used → (∃ v0, m1. valid-peb(v0, m1, mkpeb(aehdr, avhdr, buf, m2, stat = erroneous)) ∧ avhdr.sqn = (valid-sqns(v0, m1, apebs, m) ∪ (v = v0 ∧ n = m1 ⊃ {avhdr0.sqn} ;∅)).max))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
# apebs = # wlar, apebs[m] = mkpeb(aehdr0, avhdr0, buf0, m3, boolvar0), apebs[n0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), wlar[n0] = wl-entry(m4, stat), n0 + 1 < # wlar, n0 < # wlar, m < # wlar, n0 < m, valid-peb(v, n, mkpeb(aehdr0, avhdr0, buf0, m3, boolvar0)), valid-sqns(v, n, apebs, m) ≠ ∅ → avhdr0.sqn < valid-sqns(v, n, apebs, m).max, ∀ n0. 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 ↔ boolvar) ∧ (stat = free → avhdr = empty) ∧ (stat ≠ erroneous ∧ stat ≠ erasing → aehdr = aechdr(m4)) ∧ ( stat = used → (∃ v0, m0. valid-peb(v0, m0, mkpeb(aehdr, avhdr, buf, m2, false)) ∧ avhdr.sqn = (valid-sqns(v0, m0, apebs, m) ∪ (v = v0 ∧ n = m0 ⊃ {avhdr0.sqn} ;∅)).max))

Rule argument

Additional information

Used simplifier rules: ⊦ used ≠ erroneous; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m +1 = m + 1; (s)% ⊦ m < n → n ≠ 0; (s)% ⊦ wl-entry(m, stat) = wl-entry(m0, stat0) ↔ m = m0 ∧ stat = stat0; (ws)%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)% ⊦ m ≠ n → wlar[n, wle][m] = wlar[m]; (s)