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Proof step 31 from proof valid-eraseq-stronger-next (previous step)

avhdr.sqn = avhdr0.sqn, apebs[m1] = mkpeb(aehdr, avhdr, buf, m2, boolvar), apebs[m] = mkpeb(aehdr0, avhdr0, buf0, m3, boolvar0), 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, mkpeb(aehdr0, avhdr0, buf0, m3, boolvar0)), ∀ 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, valid-sqns(v, m0, apebs, m) = ∅, avhdr0.sqn < valid-sqns(v, m0, apebs, m).max, m1 ∈ q0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
avhdr.sqn = avhdr0.sqn, apebs[m] = mkpeb(aehdr0, avhdr0, buf0, m3, boolvar0), apebs[m1] = mkpeb(aehdr, avhdr, buf, m2, boolvar), valid-sqns(v, m0, apebs, m).max < avhdr0.sqn, 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, mkpeb(aehdr0, avhdr0, buf0, m3, boolvar0)), 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) ⊦ avhdr0.sqn = valid-sqns(v, m0, apebs, m).max, valid-sqns(v, m0, apebs, m) = ∅, m1 ∈ q0

Rule argument

Additional information

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