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Proof step 15 from proof valid-sqns-nonempty-extract-max-h (previous step)

apebs[n].vidhdr.sqn = valid-sqns(v, m, apebs, n0).max, apebs[n0] = mkpeb(aehdr, avhdr, buf, m0, boolvar), n < # apebs, n < n0, avhdr.sqn < valid-sqns(v, m, apebs, n0).max, n0 < # apebs, n + 1 < # apebs, valid-peb(v, m, apebs[n]), valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)), ∀ apebs, v, m. n0 ≤ # apebs → valid-sqns(v, m, apebs, n0) = ∅ ∨ (∃ n1. n1 < n0 ∧ valid-peb(v, m, apebs[n1]) ∧ apebs[n1].vidhdr.sqn = valid-sqns(v, m, apebs, n0).max) ⊦ avhdr.sqn = valid-sqns(v, m, apebs, n0).max, valid-sqns(v, m, apebs, n0) = ∅, ∃ n. ¬ n0 < n ∧ valid-peb(v, m, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m, apebs, n0).max

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 16:
avhdr0.sqn = valid-sqns(v, m, apebs, n0).max, apebs[n0] = mkpeb(aehdr, avhdr, buf, m0, boolvar), apebs[n] = mkpeb(aehdr0, avhdr0, buf0, m1, boolvar0), n + 1 < # apebs, n0 < # apebs, avhdr.sqn < valid-sqns(v, m, apebs, n0).max, n < n0, n < # apebs, valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)), valid-peb(v, m, apebs[n]), ∀ apebs, v, m. n0 ≤ # apebs → valid-sqns(v, m, apebs, n0) = ∅ ∨ (∃ n1. n1 < n0 ∧ valid-peb(v, m, apebs[n1]) ∧ apebs[n1].vidhdr.sqn = valid-sqns(v, m, apebs, n0).max) ⊦ avhdr.sqn = valid-sqns(v, m, apebs, n0).max, valid-sqns(v, m, apebs, n0) = ∅, ∃ n. ¬ n0 < n ∧ valid-peb(v, m, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m, apebs, n0).max

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[n], aehdr0, avhdr0, buf0, m1, 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[n], aehdr0, avhdr0, buf0, m1, boolvar0