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Proof step 23 from proof valid-global-sqn-write-valid (previous step)

apebs[m] = mkpeb(aehdr, avhdr, buf0, m0, boolvar0), m < # apebs, valid-peb(mkpeb(aehdr, avhdr, buf0, m0, boolvar0)), valid-peb(mkpeb(aehdr, avhdr, buf1, m1, boolvar1)), n ≤ ( (valid-sqns(v, m2, apebs) \ (valid-peb(v, m2, mkpeb(aehdr, avhdr, buf0, m0, boolvar0)) ⊃ {avhdr.sqn} ;∅)) ∪ (valid-peb(v, m2, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)) ⊃ {avhdr.sqn} ;∅) ).max, ∀ v, m2. valid-sqns(v, m2, apebs) ≠ ∅ → valid-sqns(v, m2, apebs).max < n ⊦ (valid-sqns(v, m2, apebs) \ ∅) ∪ (valid-peb(v, m2, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)) ⊃ {avhdr.sqn} ;∅) = ∅, valid-peb(v, m2, mkpeb(aehdr, avhdr, buf0, m0, boolvar0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
apebs[m] = mkpeb(aehdr, avhdr, buf0, m0, boolvar0), m < # apebs, valid-peb(mkpeb(aehdr, avhdr, buf1, m1, boolvar1)), valid-peb(mkpeb(aehdr, avhdr, buf0, m0, boolvar0)), n ≤ (valid-sqns(v, m2, apebs) ∪ (valid-peb(v, m2, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)) ⊃ {avhdr.sqn} ;∅)).max, ∀ v, m2. valid-sqns(v, m2, apebs) ≠ ∅ → valid-sqns(v, m2, apebs).max < n ⊦ valid-sqns(v, m2, apebs) ∪ (valid-peb(v, m2, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)) ⊃ {avhdr.sqn} ;∅) = ∅, v = avhdr.vol ∧ m2 = avhdr.leb

Rule argument

Additional information

Used simplifier rules: ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)%⊦ valid-peb(apeb) → (valid-peb(v, m, apeb) ↔ v = apeb.vidhdr.vol ∧ m = apeb.vidhdr.leb); (ss)% ⊦ bag \ ∅ = bag; (s)