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

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
# apebs = # wlar, apebs[m0].vidhdr.sqn = valid-sqns(v, n, apebs, m).max, apebs[m] = mkpeb(aehdr, avhdr, buf, m3, boolvar), m0 < # wlar, m < # wlar, valid-sqns(v, n, apebs, m).max < avhdr.sqn, m0 < m, n0 < # wlar, m0 + 1 < # wlar, valid-peb(v, n, mkpeb(aehdr, avhdr, buf, m3, boolvar)), valid-peb(v, n, apebs[m0]), n0 ≤ m, ∀ v, m. unique-elems(valid-sqns(v, m, apebs)), ∀ 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, m2. valid-peb(v0, m2, apebs[n0]) ∧ apebs[n0].vidhdr.sqn = valid-sqns(v0, m2, apebs, m).max)) ⊦ (wlar[m, wl-entry(aehdr.ec, used)][m0, wl-entry(m1, erasing)][n0].status = erroneous ↔ apebs[n0].bad) ∧ (wlar[m, wl-entry(aehdr.ec, used)][m0, wl-entry(m1, erasing)][n0].status = free → apebs[n0].vidhdr = empty) ∧ ( wlar[m, wl-entry(aehdr.ec, used)][m0, wl-entry(m1, erasing)][n0].status ≠ erroneous ∧ wlar[m, wl-entry(aehdr.ec, used)][m0, wl-entry(m1, erasing)][n0].status ≠ erasing → apebs[n0].echdr = aechdr(wlar[m, wl-entry(aehdr.ec, used)][m0, wl-entry(m1, erasing)][n0].ec)) ∧ ( wlar[m, wl-entry(aehdr.ec, used)][m0, wl-entry(m1, erasing)][n0].status = used → (∃ v0, m2. valid-peb(v0, m2, apebs[n0]) ∧ apebs[n0].vidhdr.sqn = (valid-sqns(v0, m2, apebs, m) ∪ (v = v0 ∧ n = m2 ⊃ {avhdr.sqn} ;∅)).max))

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic