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Proof step 10 from proof valid-sqns-extract2-sqn-h (previous step)

apebs[n0] = mkpeb(aehdr, avhdr, buf, m0, boolvar), apebs[n1] = mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0), m1 < # apebs, n0 < # apebs, n1 < # apebs, valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)), valid-peb(v, m, mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0)), n0 ≤ m1, n1 ≤ m1, 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 ++ avhdr0.sqn

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
apebs[n0] = mkpeb(aehdr, avhdr, buf, m0, boolvar), apebs[n1] = mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0), m1 < # apebs, n0 < # apebs, n1 < # apebs, valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)), valid-peb(v, m, mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0)), n0 ≤ m1, n1 ≤ m1, n1 < m1 ∧ n0 < m1 → valid-sqns(v, m, apebs, m1) = bag ++ avhdr.sqn ++ avhdr0.sqn ⊦ n0 = n1, ∃ bag. valid-sqns(v, m, apebs, m1) ∪ (valid-peb(v, m, apebs[m1]) ⊃ {apebs[m1].vidhdr.sqn} ;∅) = bag ++ avhdr.sqn ++ avhdr0.sqn

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)% ⊦ m < n → m ≤ n; (s)