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Proof step 2 from proof lf-valid-recs-max (previous step)

# apebs = # wlar, recs[v × n] = recovery-entry(m0, m1), 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, m ≤ # apebs ⊦ m1 = valid-sqns(v, n, apebs, m).max

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
# apebs = # wlar, recs[v × n] = recovery-entry(m0, apebs[m0].vidhdr.sqn), m0 < m, m0 < # wlar, valid-peb(v, n, apebs[m0]), 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, m ≤ # wlar ⊦ apebs[m0].vidhdr.sqn = valid-sqns(v, n, apebs, m).max

Rule argument

Additional information

Used simplifier rules: 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]);%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (s)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)