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Proof step 44 from proof prepost-scan-all (previous step)

# wlar = n0 + vtblpnum, # apebs = n0 + vtblpnum, err = ESUCCESS, err = err0, vtblpnum0 = vtblpnum, apebs[vtblpnum].bad, nx < vtblpnum, vtblpnum < # apebs, vtblpnum0 < # wlar, bflipset-cons(bflipset, subarray(wlar, 0, vtblpnum)), indices-erasing(wlar, nx), ubi-io-inv(apebs), unique-sqns(apebs), valid-eraseq(subarray(wlar, 0, vtblpnum), q), valid-eraseq-stronger(subarray(apebs, 0, vtblpnum), q), valid-global-sqn(subarray(apebs, 0, vtblpnum), sqnum), valid-recs(subarray(apebs, 0, vtblpnum), subarray(wlar, 0, vtblpnum), recs), valid-recs-sqns(apebs, recs), valid-wl(subarray(apebs, 0, vtblpnum), subarray(wlar, 0, vtblpnum)), ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ n0 = 0, dups(nx), vtblpnum0 + 1 ≤ # apebs ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → # apebs = # wlar[vtblpnum0, wl-entry(wlar[vtblpnum0].ec, erroneous)] ∧ ¬ dups(nx) ∧ nx < vtblpnum0 + 1 ∧ indices-erasing(wlar[vtblpnum0, wl-entry(wlar[vtblpnum0].ec, erroneous)], nx) ∧ valid-global-sqn(subarray(apebs, 0, vtblpnum0 + 1), sqnum) ∧ valid-eraseq(subarray(wlar[vtblpnum0, wl-entry(wlar[vtblpnum0].ec, erroneous)], 0, vtblpnum0 + 1), q) ∧ bflipset-cons(bflipset, subarray(wlar[vtblpnum0, wl-entry(wlar[vtblpnum0].ec, erroneous)], 0, vtblpnum0 + 1)) ∧ valid-eraseq-stronger(subarray(apebs, 0, vtblpnum0 + 1), q) ∧ valid-wl(subarray(apebs, 0, vtblpnum0 + 1), subarray(wlar[vtblpnum0, wl-entry(wlar[vtblpnum0].ec, erroneous)], 0, vtblpnum0 + 1)) ∧ valid-recs-sqns(apebs, recs) ∧ valid-recs(subarray(apebs, 0, vtblpnum0 + 1), subarray(wlar[vtblpnum0, wl-entry(wlar[vtblpnum0].ec, erroneous)], 0, vtblpnum0 + 1), recs)) ∧ # apebs < n0 + vtblpnum0 + 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ n < n; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m < n + 1 ↔ ¬ n < m; (s)%m < # apebs, # wlar = # apebs, stat ≠ used ⊦ valid-recs(subarray(apebs, 0, m), subarray(wlar, 0, m), recs) → valid-recs (subarray(apebs, 0, m + 1), subarray(wlar[m, wl-entry(m0, stat)], 0, m + 1), recs); (ss)% ⊦ used ≠ erroneous; (s)%m < # apebs ⊦ valid-eraseq-stronger(subarray(apebs, 0, m), q) → valid-eraseq-stronger(subarray(apebs, 0, m + 1), q); (ss)%n < # wlar ⊦ bflipset-cons(bflipset, subarray(wlar, 0, n)) → bflipset-cons(bflipset, subarray(wlar[n, wle], 0, n + 1)); (ss)% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)%n < # wlar, stat ≠ erasing ⊦ valid-eraseq(subarray(wlar, 0, n), q) → valid-eraseq(subarray(wlar[n, wl-entry(m, stat)], 0, n + 1), q); (ss)% ⊦ erroneous ≠ erasing; (s)% ⊦ m < m + n ↔ n ≠ 0; (s)%⊦ nx < m ∧ indices-erasing(wlar, nx) → indices-erasing(wlar[m, wle], nx); (ss)% ⊦ nx < m → nx < m + n; (ss)% ⊦ # wlar[n, wle] = # wlar; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≤ n ↔ m < n; (s)% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)