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Proof step 38 from proof valid-wl-next-valid-update (previous step)

# apebs = # wlar, avhdr1.sqn = avhdr0.sqn, wlar[n0] = wl-entry(m7, used), apebs[m0] = mkpeb(aehdr0, avhdr0, buf0, m4, boolvar0), apebs[m] = mkpeb(aehdr, avhdr, buf, m3, boolvar), apebs[n0] = mkpeb(aechdr(m7), avhdr1, buf1, m5, false), valid-sqns(v0, m1, apebs, m).max < avhdr.sqn, n0 < m, m0 < # wlar, m < # wlar, avhdr0.sqn < avhdr.sqn, m0 < m, n0 < # wlar, m0 + 1 < # wlar, n0 + 1 < # wlar, (bag ++ avhdr0.sqn).max < avhdr.sqn, unique-elems(valid-sqns(v0, m1, apebs)), valid-peb(v0, m1, mkpeb(aechdr(m7), avhdr1, buf1, m5, false)), valid-peb(v0, m1, mkpeb(aehdr, avhdr, buf, m3, boolvar)), valid-peb(v0, m1, mkpeb(aehdr0, avhdr0, buf0, m4, boolvar0)), (bag ++ avhdr0.sqn).max ≤ avhdr0.sqn ⊦ avhdr0.sqn = avhdr.sqn, n0 = m0, n0 = m, valid-sqns(v0, m1, apebs, m) ⊆ valid-sqns(v0, m1, apebs)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: sqns name: valid-sqns-subseteq seq: ⊦ n ≤ # apebs → valid-sqns(v, m, apebs, n) ⊆ valid-sqns(v, m, apebs) subst: [n, apebs, m, v] → [m, apebs, m1, v0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]% ⊦ m +1 = m + 1; (s)% ⊦ ¬ m + n < m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: m, apebs, m1, v0