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Proof step 3 from proof valid-peb-in-sqnums-h (previous step)

apebs[n0] = mkpeb(aehdr, avhdr, buf, m0, boolvar), n0 < n1, n0 < # apebs, valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)), n1 ≤ # apebs ⊦ avhdr.sqn ∈ valid-sqns(v, m, apebs, n1)

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 4:
apebs[n0] = mkpeb(aehdr, avhdr, buf, m0, boolvar), n0 < # apebs, n0 < n +1, valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)), n +1 ≤ # apebs, ∀ apebs, n0, aehdr, avhdr, buf, m0, boolvar, v, m. apebs[n0] = mkpeb(aehdr, avhdr, buf, m0, boolvar) ∧ n0 < n ∧ n0 < # apebs ∧ valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)) ∧ n ≤ # apebs → avhdr.sqn ∈ valid-sqns(v, m, apebs, n) ⊦ avhdr.sqn ∈ valid-sqns(v, m, apebs, n +1)

Rule argument

term: n1

Additional information

Used simplifier rules: nat freely generated by 0, +1;;% ⊦ 0 ≤ m; (s)% ⊦ ¬ m < 0; (s)