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Proof step 3 from proof valid-global-sqn-add-valid (previous step)

m < # apebs, apeb.vidhdr.sqn < n, apeb.vidhdr.sqn < valid-sqns(v, m0, apebs[m, apeb]).max, valid-peb(apeb), n ≤ valid-sqns(v, m0, apebs[m, apeb]).max, ∀ v, m0. valid-sqns(v, m0, apebs) ≠ ∅ → valid-sqns(v, m0, apebs).max < n ⊦ valid-sqns(v, m0, apebs[m, apeb]) = ∅

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
apeb = mkpeb(aehdr, avhdr, buf, m1, boolvar), avhdr.sqn < valid-sqns(v, m0, apebs[m, apeb]).max, avhdr.sqn < n, m < # apebs, valid-peb(apeb), n ≤ valid-sqns(v, m0, apebs[m, apeb]).max, ∀ v, m0. valid-sqns(v, m0, apebs) ≠ ∅ → valid-sqns(v, m0, apebs).max < n ⊦ valid-sqns(v, m0, apebs[m, apeb]) = ∅

Rule argument

spec: apeb name: elim seq: ⊦ ( ( (aehdr = apeb.echdr ∧ avhdr = apeb.vidhdr) ∧ buf = apeb.data) ∧ m = apeb.fill) ∧ (boolvar ↔ apeb.bad) ↔ apeb = mkpeb(aehdr, avhdr, buf, m, boolvar) subst: [apeb, aehdr, avhdr, buf, m, boolvar] → [apeb, aehdr, avhdr, buf, m2, boolvar]

Additional information

Used simplifier rules: ⊦ ( ((aehdr = apeb.echdr ∧ avhdr = apeb.vidhdr) ∧ buf = apeb.data) ∧ m = apeb.fill) ∧ (boolvar ↔ apeb.bad) ↔ apeb = mkpeb(aehdr, avhdr, buf, m, boolvar); (elim) Used terms: apeb, aehdr, avhdr, buf, m2, boolvar