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Proof step 19 from proof valid-eraseq-stronger-next (previous step)

avhdr.sqn = (valid-sqns(v, m0, apebs, m) ∪ {apebs[m].vidhdr.sqn} ).max, apebs[m1] = mkpeb(aehdr, avhdr, buf, m2, boolvar), m1 < # apebs, m < # apebs, m1 < m, m1 + 1 < # apebs, valid-eraseq-stronger(subarray(apebs, 0, m), q0), valid-eraseq-stronger(subarray(apebs, 0, m + 1), q0), valid-peb(v, m0, mkpeb(aehdr, avhdr, buf, m2, boolvar)), valid-peb(v, m0, apebs[m]), ∀ m, apebs. m < # apebs ∧ valid-eraseq-stronger(subarray(apebs, 0, m), q0) → valid-eraseq-stronger(subarray(apebs, 0, m + 1), q0) ⊦ avhdr.sqn = valid-sqns(v, m0, apebs, m).max, m1 ∈ q0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
avhdr.sqn = (valid-sqns(v, m0, apebs, m) ++ apebs[m].vidhdr.sqn).max, apebs[m1] = mkpeb(aehdr, avhdr, buf, m2, boolvar), m1 + 1 < # apebs, m1 < m, m < # apebs, m1 < # apebs, valid-eraseq-stronger(subarray(apebs, 0, m + 1), q0), valid-eraseq-stronger(subarray(apebs, 0, m), q0), valid-peb(v, m0, apebs[m]), valid-peb(v, m0, mkpeb(aehdr, avhdr, buf, m2, boolvar)), ∀ m, apebs. m < # apebs ∧ valid-eraseq-stronger(subarray(apebs, 0, m), q0) → valid-eraseq-stronger(subarray(apebs, 0, m + 1), q0) ⊦ avhdr.sqn = valid-sqns(v, m0, apebs, m).max, m1 ∈ q0

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]% ⊦ bag ∪ {n} = bag ++ n; (s)