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Proof step 2 from proof valid-global-sqn-add-valid (previous step)

apeb.vidhdr.sqn < n, m < # apebs, valid-global-sqn(apebs, n), valid-peb(apeb) ⊦ valid-global-sqn(apebs[m, apeb], n)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
m < # apebs, apeb.vidhdr.sqn < n, apeb.vidhdr.sqn < valid-sqns(v, m0, apebs[m, apeb]).max, valid-peb(apeb), n ≤ valid-sqns(v, m0, apebs[m, apeb]).max, ∀ v, m0. valid-sqns(v, m0, apebs) ≠ ∅ → valid-sqns(v, m0, apebs).max < n ⊦ valid-sqns(v, m0, apebs[m, apeb]) = ∅

Rule argument

Additional information

Used simplifier rules: valid-global-sqn: ⊦ valid-global-sqn(apebs, n) ↔ (∀ v, m. valid-sqns(v, m, apebs) ≠ ∅ → n > valid-sqns(v, m, apebs).max);% ⊦ 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; (ss)% ⊦ m > n ↔ n < m; (s)