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Proof step 9 from proof unique-sqns-2-valid-pebs (previous step)

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, mkpeb(aehdr0, avhdr0, buf0, m3, boolvar0)), valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m2, boolvar)), m0 < # apebs ∧ m1 < # apebs ∧ m0 ≠ m1 ∧ valid-peb(v, m, apebs[m0]) ∧ valid-peb(v, m, apebs[m1]) → (∃ bag. valid-sqns(v, m, apebs) = bag ++ apebs[m0].vidhdr.sqn ++ apebs[m1].vidhdr.sqn), ∀ v, m. unique-elems(valid-sqns(v, m, apebs)) ⊦ m0 = m1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
avhdr.sqn = avhdr0.sqn, apebs[m0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), apebs[m1] = mkpeb(aehdr0, avhdr0, buf0, m3, boolvar0), valid-sqns(v, m, apebs) = bag ++ avhdr0.sqn ++ avhdr0.sqn, m1 < # apebs, m0 < # apebs, valid-peb(v, m, mkpeb(aehdr0, avhdr0, buf0, m3, boolvar0)), valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m2, boolvar)), ∀ v, m. unique-elems(valid-sqns(v, m, apebs)) ⊦ m0 = m1

Rule argument

Additional information

Used simplifier rules: ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)%⊦ valid-peb(v0, m0, apeb) → (valid-peb(v1, m1, apeb) ↔ v0 = v1 ∧ m0 = m1); (s)