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Proof step 18 from proof valid-global-sqn-next (previous step)

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))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
apebs[m] = mkpeb(aehdr, avhdr, buf, m1, boolvar), m < # apebs, n ≤ valid-sqns(v, m0, apebs, m).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))

Rule argument

Additional information

Used simplifier rules: union-com: ⊦ bag ∪ bag2 = bag2 ∪ bag; from specification bag-union[nat-bag]%union-ass: ⊦ bag ∪ bag3 ∪ bag4 = (bag ∪ bag3) ∪ bag4; from specification bag-union[nat-bag]% ⊦ ∅ ∪ bag0 = bag0; (s)