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Proof step 38 from proof valid-eraseq-stronger-prev-append-lref (previous step)

avhdr0.sqn = avhdr.sqn, apebs[m3] = mkpeb(aehdr0, avhdr0, buf0, m4, false), apebs[m] = mkpeb(aehdr, avhdr, buf, m1, boolvar), apebs[m0] = mkpeb(aehdr1, avhdr1, buf1, m5, boolvar0), valid-sqns(v0, m2, apebs, m) = bag ++ avhdr1.sqn ++ avhdr.sqn, (bag ++ avhdr1.sqn ++ avhdr.sqn).max < (bag ++ avhdr1.sqn).max, (bag ++ avhdr1.sqn ++ avhdr.sqn).max < avhdr.sqn, m3 + 1 < # apebs, m3 < m, m0 < # apebs, m0 < m, m < # apebs, m0 + 1 < # apebs, m3 < # apebs, avhdr.sqn < (bag ++ avhdr1.sqn).max, (bag ++ avhdr1.sqn ++ avhdr.sqn).max + 1 < (bag ++ avhdr1.sqn).max, valid-eraseq-stronger(subarray(apebs, 0, m + 1), q0 + eq-entry(m0, v0 × m2) '), valid-eraseq-stronger(subarray(apebs, 0, m), q0), valid-peb(v0, m2, mkpeb(aehdr, avhdr, buf, m1, boolvar)), valid-peb(v0, m2, mkpeb(aehdr1, avhdr1, buf1, m5, boolvar0)), valid-peb(v0, m2, mkpeb(aehdr0, avhdr0, buf0, m4, false)) ⊦ m0 = m3, m3 ∈ q0, m0 ∈ q0

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 ++ avhdr1.sqn] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ∅ ≠ bag ++ n; (s)% ⊦ m > n ↔ n < m; (s)% ⊦ ¬ n < n; (s)%# apebs = n ⊦ subarray(apebs, 0, n) = apebs; (s) Used terms: avhdr.sqn, bag ++ avhdr1.sqn