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Proof step 14 from proof valid-sqns-nonempty-extract-max-h (previous step)

apebs[n0] = mkpeb(aehdr, avhdr, buf, m0, boolvar), avhdr.sqn < valid-sqns(v, m, apebs, n0).max, n0 < # apebs, valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)), n0 ≤ # apebs → valid-sqns(v, m, apebs, n0) = ∅ ∨ (∃ n1. n1 < n0 ∧ valid-peb(v, m, apebs[n1]) ∧ apebs[n1].vidhdr.sqn = valid-sqns(v, m, apebs, n0).max), ∀ apebs, v, m. n0 ≤ # apebs → valid-sqns(v, m, apebs, n0) = ∅ ∨ (∃ n1. n1 < n0 ∧ valid-peb(v, m, apebs[n1]) ∧ apebs[n1].vidhdr.sqn = valid-sqns(v, m, apebs, n0).max) ⊦ avhdr.sqn = valid-sqns(v, m, apebs, n0).max, valid-sqns(v, m, apebs, n0) = ∅, ∃ n. ¬ n0 < n ∧ valid-peb(v, m, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m, apebs, n0).max

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
apebs[n].vidhdr.sqn = valid-sqns(v, m, apebs, n0).max, apebs[n0] = mkpeb(aehdr, avhdr, buf, m0, boolvar), n < # apebs, n < n0, avhdr.sqn < valid-sqns(v, m, apebs, n0).max, n0 < # apebs, n + 1 < # apebs, valid-peb(v, m, apebs[n]), valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)), ∀ apebs, v, m. n0 ≤ # apebs → valid-sqns(v, m, apebs, n0) = ∅ ∨ (∃ n1. n1 < n0 ∧ valid-peb(v, m, apebs[n1]) ∧ apebs[n1].vidhdr.sqn = valid-sqns(v, m, apebs, n0).max) ⊦ avhdr.sqn = valid-sqns(v, m, apebs, n0).max, valid-sqns(v, m, apebs, n0) = ∅, ∃ n. ¬ n0 < n ∧ valid-peb(v, m, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m, apebs, n0).max

Rule argument

Additional information

Used simplifier rules: ⊦ m +1 = m + 1; (s)% ⊦ m < n → n ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%trans: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification nat-basic%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n → m ≤ n; (s)