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Proof step 16 from proof valid-global-sqn-add-valid (previous step)

apebs[m] = mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0), avhdr.sqn < n, m < # apebs, valid-sqns(v, m0, apebs).max < n, avhdr.sqn < ((valid-sqns(v, m0, apebs) -- avhdr0.sqn) ++ avhdr.sqn).max, avhdr.sqn < (valid-sqns(v, m0, apebs) -- avhdr0.sqn).max, valid-sqns(v, m0, apebs).max < (valid-sqns(v, m0, apebs) -- avhdr0.sqn).max, valid-peb(v, m0, mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0)), valid-peb(mkpeb(aehdr, avhdr, buf, m1, boolvar)), valid-peb(v, m0, mkpeb(aehdr, avhdr, buf, m1, boolvar)), n ≤ (valid-sqns(v, m0, apebs) -- avhdr0.sqn).max ⊦ (valid-sqns(v, m0, apebs) -- avhdr0.sqn) ∪ (valid-peb(v, m0, mkpeb(aehdr, avhdr, buf, m1, boolvar)) ⊃ {avhdr.sqn} ;∅) = ∅

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
apebs[m] = mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0), valid-sqns(v, m0, apebs).max < (valid-sqns(v, m0, apebs) -- avhdr0.sqn).max, avhdr.sqn < (valid-sqns(v, m0, apebs) -- avhdr0.sqn).max, avhdr.sqn < ((valid-sqns(v, m0, apebs) -- avhdr0.sqn) ++ avhdr.sqn).max, valid-sqns(v, m0, apebs).max < n, m < # apebs, avhdr.sqn < n, valid-peb(v, m0, mkpeb(aehdr, avhdr, buf, m1, boolvar)), valid-peb(mkpeb(aehdr, avhdr, buf, m1, boolvar)), valid-peb(v, m0, mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0)), n ≤ (valid-sqns(v, m0, apebs) -- avhdr0.sqn).max ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ ∅ ≠ bag ++ n; (s)%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]% ⊦ bag ∪ {n} = bag ++ n; (s)%⊦ valid-peb(v0, m0, apeb) → (valid-peb(v1, m1, apeb) ↔ v0 = v1 ∧ m0 = m1); (s)