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Proof step 7 from proof valid-sqns-extract2-sqn-h (previous step)

apebs[n0] = mkpeb(aehdr, avhdr, buf, m0, boolvar), n1 < # apebs, n0 < # apebs, m1 < # apebs, valid-peb(v, m, apebs[n1]), valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)), n1 ≤ m1, n0 ≤ m1, ∀ n1, n0, apebs, v, m. n1 < m1 ∧ n0 < m1 ∧ n1 < # apebs ∧ n0 < # apebs ∧ valid-peb(v, m, apebs[n1]) ∧ valid-peb(v, m, apebs[n0]) ∧ m1 ≤ # apebs → n0 = n1 ∨ (∃ bag. valid-sqns(v, m, apebs, m1) = bag ++ apebs[n0].vidhdr.sqn ++ apebs[n1].vidhdr.sqn) ⊦ n0 = n1, ∃ bag. valid-sqns(v, m, apebs, m1) ∪ (valid-peb(v, m, apebs[m1]) ⊃ {apebs[m1].vidhdr.sqn} ;∅) = bag ++ avhdr.sqn ++ apebs[n1].vidhdr.sqn

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

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] → [apebs[n1], aehdr0, avhdr0, buf0, m2, boolvar0]

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: apebs[n1], aehdr0, avhdr0, buf0, m2, boolvar0