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Proof step 11 from proof valid-global-sqn-next (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
apebs[m] = mkpeb(aehdr, avhdr, buf, m1, boolvar), m < # apebs, (valid-sqns(v, m0, apebs, m) ++ avhdr.sqn).max < n, (valid-sqns(v, m0, apebs, m) ++ avhdr.sqn).max < avhdr.sqn, valid-peb(v, m0, mkpeb(aehdr, avhdr, buf, m1, boolvar)), n ≤ avhdr.sqn, ∀ v, m0. valid-sqns(v, m0, apebs, m) ≠ ∅ → valid-sqns(v, m0, apebs, m).max < n ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ ∅ ≠ 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)