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Proof step 424 from proof prepost-scan-all (previous step)

# apebs = n0 + vtblpnum, # wlar0 = n0 + vtblpnum, apebs[vtblpnum] = mkpeb(aechdr(m), avidhdr(v, m1, m2, 0, m4), buf1, m0, false), nx < vtblpnum, vtblpnum < recs[v × m1].pnum, bflipset-cons(bflipset, subarray(wlar0, 0, vtblpnum)), indices-erasing(wlar0, nx), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aechdr(m), avidhdr(v, m1, m2, 0, m4), buf1, m0, false)), unique-sqns(apebs), valid-eraseq(subarray(wlar0, 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(wlar0, 0, vtblpnum), recs), valid-recs-sqns(apebs, recs), valid-wl(subarray(apebs, 0, vtblpnum), subarray(wlar0, 0, vtblpnum)), v × m1 ∈ recs, n0 + vtblpnum ≤ recs[v × m1].pnum, recs[v × m1].sqn ≤ m2 ⊦ n0 = 0, dups(nx)

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: recovery-entry name: elim seq: ⊦ m = rec.pnum ∧ m0 = rec.sqn ↔ rec = recovery-entry(m, m0) subst: [rec, m, m0] → [recs[v × m1], m3, m5]

Additional information

Used simplifier rules: lf-valid-recs-max: m ≤ # apebs, # apebs = # wlar ⊦ valid-recs(subarray(apebs, 0, m), subarray(wlar, 0, m), recs) ∧ valid-recs-sqns(apebs, recs) ∧ valid-wl(subarray(apebs, 0, m), subarray(wlar, 0, m)) ∧ v × n ∈ recs ∧ recs[v × n] = recovery-entry(m0, m1) → m1 = valid-sqns(v, n, apebs, m).max;%lf-valid-recs-notin-eraseq: ⊦ v × m ∈ recs ∧ recs[v × m] = recovery-entry(n0, n1) ∧ valid-recs(apebs, wlar, recs) ∧ valid-eraseq(wlar, q) → ¬ n0 ∈ q;%lf-valid-recs-sqns-vidhdr: ⊦ v × m ∈ recs ∧ recs[v × m] = recovery-entry(n0, n1) ∧ valid-recs-sqns(apebs, recs) → apebs[n0].vidhdr.sqn = n1;%lf-valid-recs-in-apebs: m0 ≤ # apebs ⊦ v × m ∈ recs ∧ recs[v × m] = recovery-entry(n0, n1) ∧ valid-recs(subarray(apebs, 0, m0), subarray(wlar, 0, m0), recs) → n0 < m0;%lf-valid-recs-valid-peb: m0 ≤ # apebs, # apebs = # wlar ⊦ v × m ∈ recs ∧ recs[v × m] = recovery-entry(n0, n1) ∧ valid-recs(subarray(apebs, 0, m0), subarray(wlar, 0, m0), recs) ∧ valid-wl(subarray(apebs, 0, m0), subarray(wlar, 0, m0)) → valid-peb(v, m, apebs[n0]);%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≤ m + n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ ¬ m + n < m; (s)% ⊦ m < n → n ≠ 0; (s)% ⊦ m < n → ¬ n < m; (s)% ⊦ m = rec.pnum ∧ m0 = rec.sqn ↔ rec = recovery-entry(m, m0); (elim) Used terms: recs[v × m1], m3, m5