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Proof step 24 from proof valid-wl-write-valid (previous step)

# apebs = # wlar, wlar[m] = wl-entry(m2, used), apebs[m] = mkpeb(aechdr(m2), avhdr0, buf, m3, false), valid-sqns(v, m5, apebs).max < avhdr0.sqn, m < # wlar, valid-peb(v, m5, mkpeb(aechdr(m2), avhdr0, buf, m3, false)), valid-peb(mkpeb(aechdr(m2), avhdr0, buf2, m6, false)), valid-peb(v, m5, mkpeb(aechdr(m2), avhdr0, buf2, m6, false)), valid-peb(mkpeb(aechdr(m2), avhdr0, buf, m3, false)) ⊦ avhdr0.sqn = valid-sqns(v, m5, apebs).max

User applied rule apply lemma

And obtained the following new goals

Rule argument

spec: sqns name: valid-sqns-extract-sqn seq: n < # apebs ⊦ valid-peb(v, m, apebs[n]) → (∃ bag. valid-sqns(v, m, apebs) = bag ++ apebs[n].vidhdr.sqn) subst: [n, apebs, v, m] → [m, apebs, v, m5]

Additional information

Used simplifier rules: ⊦ valid-peb(v0, m0, apeb) → (valid-peb(v1, m1, apeb) ↔ v0 = v1 ∧ m0 = m1); (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ m = (bag ++ m).max ↔ ¬(bag ≠ ∅ ∧ m < bag.max); (s)% ⊦ bag ≠ ∅ → (bag ++ m).max = (bag.max > m ⊃ bag.max;m); (s)% ⊦ m > n ↔ n < m; (s)% ⊦ m < n → ¬ n < m; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat[encoding-nat]%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat[encoding-nat]% ⊦ ¬ n < n; (s) Used terms: m, apebs, v, m5