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Proof step 15 from proof valid-eraseq-stronger-prev-append-lref (previous step)

avhdr0.sqn = avhdr.sqn, apebs[m] = mkpeb(aehdr, avhdr, buf, m1, boolvar), apebs[m0] = mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0), valid-sqns(v, n, apebs, m) = bag ++ avhdr.sqn, m0 < # apebs, (bag ++ avhdr.sqn).max < avhdr.sqn, m0 < m, m < # apebs, m0 + 1 < # apebs, valid-peb(v, n, mkpeb(aehdr, avhdr, buf, m1, boolvar)), valid-peb(v, n, mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0)) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

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, bag] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m > n ↔ n < m; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m < n → ¬ n < m; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (s)% ⊦ ¬ n < n; (s) Used terms: avhdr.sqn, bag