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Proof step 22 from proof valid-wl-markbad (previous step)

# apebs = # wlar, avhdr0.sqn = (bag ++ avhdr0.sqn ++ avhdr.sqn).max, wlar[n] = wl-entry(m5, used), apebs[n] = mkpeb(aechdr(m5), avhdr0, buf0, m3, false), apebs[m] = mkpeb(aehdr, avhdr, buf, m0, boolvar), valid-sqns(v, m1, apebs) = bag ++ avhdr0.sqn ++ avhdr.sqn, avhdr0.sqn < bag.max, n < # wlar, m < # wlar, valid-peb(v, m1, mkpeb(aechdr(m5), avhdr0, buf0, m3, false)), valid-peb(v, m1, mkpeb(aehdr, avhdr, buf, m0, boolvar)) ⊦ bag = ∅, n = m

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 ++ avhdr0.sqn] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ∅ ≠ bag ++ n; (s)% ⊦ bag ≠ ∅ → (bag ++ m).max = (bag.max > m ⊃ bag.max;m); (s)% ⊦ m > n ↔ n < m; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ ¬ n < n; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ m ≤ n → (n < m ↔ false); (s) Used terms: avhdr.sqn, bag ++ avhdr0.sqn