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Proof step 12 from proof valid-global-sqn-next (previous step)

apebs[m] = mkpeb(aehdr, avhdr, buf, m1, boolvar), m < # apebs, (valid-sqns(v, m0, apebs, m) ++ avhdr.sqn).max < n, (valid-sqns(v, m0, apebs, m) ++ avhdr.sqn).max < avhdr.sqn, valid-peb(v, m0, mkpeb(aehdr, avhdr, buf, m1, boolvar)), n ≤ avhdr.sqn, ∀ v, m0. valid-sqns(v, m0, apebs, m) ≠ ∅ → valid-sqns(v, m0, apebs, m).max < n ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ (bag ++ n).max = (bag = ∅ ⊃ n;(bag.max > n ⊃ bag.max;n))

Rule argument

spec: bag-max name: max-rec seq: ⊦ (bag ++ n).max = (bag = ∅ ⊃ n;(bag.max > n ⊃ bag.max;n)) subst: [n, bag] → [avhdr.sqn, valid-sqns(v, m0, apebs, m)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m > n ↔ n < m; (s)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ m < n → n ≠ 0; (s)% ⊦ m < n → ¬ n < m; (s)% ⊦ ¬ n < n; (s) Used terms: avhdr.sqn, valid-sqns(v, m0, apebs, m)