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Proof step 5 from proof unique-sqns-2-valid-pebs (previous step)

avhdr.sqn = apebs[m1].vidhdr.sqn, apebs[m0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), m0 < # apebs, m1 < # apebs, valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m2, boolvar)), valid-peb(v, m, apebs[m1]), ∀ v, m. unique-elems(valid-sqns(v, m, apebs)) ⊦ m0 = m1

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
avhdr.sqn = avhdr0.sqn, apebs[m0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), apebs[m1] = mkpeb(aehdr0, avhdr0, buf0, m3, boolvar0), m1 < # apebs, m0 < # apebs, valid-peb(v, m, apebs[m1]), valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m2, boolvar)), ∀ v, m. unique-elems(valid-sqns(v, m, apebs)) ⊦ m0 = m1

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[m1], aehdr0, avhdr0, buf0, m3, 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[m1], aehdr0, avhdr0, buf0, m3, boolvar0