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Proof step 17 from proof valid-global-sqn-add-valid (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ (bag ++ n).max = (bag = ∅ ⊃ n;(bag.max > n ⊃ bag.max;n))
Proof step 19:
apebs[m] = mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0), avhdr.sqn < n, m < # apebs, valid-sqns(v, m0, apebs).max < n, avhdr.sqn < (valid-sqns(v, m0, apebs) -- avhdr0.sqn = ∅ ⊃ avhdr.sqn ;((valid-sqns(v, m0, apebs) -- avhdr0.sqn).max > avhdr.sqn ⊃ (valid-sqns(v, m0, apebs) -- avhdr0.sqn).max;avhdr.sqn) ), avhdr.sqn < (valid-sqns(v, m0, apebs) -- avhdr0.sqn).max, valid-sqns(v, m0, apebs).max < (valid-sqns(v, m0, apebs) -- avhdr0.sqn).max, valid-peb(v, m0, mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0)), valid-peb(mkpeb(aehdr, avhdr, buf, m1, boolvar)), valid-peb(v, m0, mkpeb(aehdr, avhdr, buf, m1, boolvar)), n ≤ (valid-sqns(v, m0, apebs) -- avhdr0.sqn).max ⊦

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) -- avhdr0.sqn] flags: <all paths>

Additional information

Used terms: avhdr.sqn, valid-sqns(v, m0, apebs) -- avhdr0.sqn