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Proof step 10 from proof valid-global-sqn-next-max (previous step)

apebs[m] = mkpeb(aehdr, avidhdr(v, m0, m1, m2, m4), buf, m3, false), n < valid-sqns(v0, m5, apebs, m).max, m < # apebs, m1 < (valid-sqns(v0, m5, apebs, m) ++ m1).max, valid-peb(v0, m5, mkpeb(aehdr, avidhdr(v, m0, m1, m2, m4), buf, m3, false)), valid-peb(mkpeb(aehdr, avidhdr(v, m0, m1, m2, m4), buf, m3, false)), n ≤ m1, ∀ v0, m5. valid-sqns(v0, m5, apebs, m) ≠ ∅ → valid-sqns(v0, m5, apebs, m).max < n ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ (bag ++ n).max = (bag = ∅ ⊃ n;(bag.max > n ⊃ bag.max;n))
Proof step 12:
apebs[m] = mkpeb(aehdr, avidhdr(v, m0, m1, m2, m4), buf, m3, false), m1 < (valid-sqns(v0, m5, apebs, m) = ∅ ⊃ m1;(valid-sqns(v0, m5, apebs, m).max > m1 ⊃ valid-sqns(v0, m5, apebs, m).max;m1)), m < # apebs, n < valid-sqns(v0, m5, apebs, m).max, valid-peb(mkpeb(aehdr, avidhdr(v, m0, m1, m2, m4), buf, m3, false)), valid-peb(v0, m5, mkpeb(aehdr, avidhdr(v, m0, m1, m2, m4), buf, m3, false)), n ≤ m1, ∀ v0, m5. valid-sqns(v0, m5, apebs, m) ≠ ∅ → valid-sqns(v0, m5, apebs, m).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] → [m1, valid-sqns(v0, m5, apebs, m)] flags: <all paths>

Additional information

Used terms: m1, valid-sqns(v0, m5, apebs, m)