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Proof step 14 from proof valid-global-sqn-next (previous step)

apebs[m] = mkpeb(aehdr, avhdr, buf, m1, boolvar), m < # apebs, ∀ v, m0. valid-sqns(v, m0, apebs, m) ≠ ∅ → valid-sqns(v, m0, apebs, m).max < n, ¬ valid-peb(mkpeb(aehdr, avhdr, buf, m1, boolvar)) ∨ avhdr.sqn < n ⊦ ∀ v, m0. valid-sqns(v, m0, apebs, m) ∪ (valid-peb(v, m0, mkpeb(aehdr, avhdr, buf, m1, boolvar)) ⊃ {avhdr.sqn} ;∅) ≠ ∅ → (valid-sqns(v, m0, apebs, m) ∪ (valid-peb(v, m0, mkpeb(aehdr, avhdr, buf, m1, boolvar)) ⊃ {avhdr.sqn} ;∅)).max < n

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
apebs[m] = mkpeb(aehdr, avhdr, buf, m1, boolvar), m < # apebs, n ≤ (valid-sqns(v, m0, apebs, m) ∪ (valid-peb(v, m0, mkpeb(aehdr, avhdr, buf, m1, boolvar)) ⊃ {avhdr.sqn} ;∅)).max, ∀ v, m0. valid-sqns(v, m0, apebs, m) ≠ ∅ → valid-sqns(v, m0, apebs, m).max < n, ¬ valid-peb(mkpeb(aehdr, avhdr, buf, m1, boolvar)) ∨ avhdr.sqn < n ⊦ valid-sqns(v, m0, apebs, m) ∪ (valid-peb(v, m0, mkpeb(aehdr, avhdr, buf, m1, boolvar)) ⊃ {avhdr.sqn} ;∅) = ∅

Rule argument

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)