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Proof step 12 from proof valid-global-sqn-next-max (previous step)

apebs[m] = mkpeb(aehdr, avidhdr(v, m0, m1, m2, m4), buf, m3, false), m1 < (valid-sqns(v0, m5, apebs, m) = ∅ ⊃ m1;(valid-sqns(v0, m5, apebs, m).max > m1 ⊃ valid-sqns(v0, m5, apebs, m).max;m1)), m < # apebs, n < valid-sqns(v0, m5, apebs, m).max, valid-peb(mkpeb(aehdr, avidhdr(v, m0, m1, m2, m4), buf, m3, false)), valid-peb(v0, m5, mkpeb(aehdr, avidhdr(v, m0, m1, m2, m4), buf, m3, false)), n ≤ m1, ∀ v0, m5. valid-sqns(v0, m5, apebs, m) ≠ ∅ → valid-sqns(v0, m5, apebs, m).max < n ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
apebs[m] = mkpeb(aehdr, avidhdr(v, m0, m1, m2, m4), buf, m3, false), n < (valid-sqns(v0, m5, apebs, m) = ∅ ⊃ m1;valid-sqns(v0, m5, apebs, m).max), n < valid-sqns(v0, m5, apebs, m).max, m < # apebs, m1 < (valid-sqns(v0, m5, apebs, m) = ∅ ⊃ m1;(m1 < valid-sqns(v0, m5, apebs, m).max ⊃ valid-sqns(v0, m5, apebs, m).max;m1)), valid-peb(v0, m5, mkpeb(aehdr, avidhdr(v, m0, m1, m2, m4), buf, m3, false)), valid-peb(mkpeb(aehdr, avidhdr(v, m0, m1, m2, m4), buf, m3, false)), n ≤ m1, ∀ v0, m5. valid-sqns(v0, m5, apebs, m) ≠ ∅ → valid-sqns(v0, m5, apebs, m).max < n ⊦

Rule argument

Additional information

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