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Proof step 21 from proof valid-wl-write-valid (previous step)

# apebs = # wlar, valid-sqns(v, m5, apebs) -- avhdr0.sqn = ∅, wlar[m] = wl-entry(m2, used), apebs[m] = mkpeb(aechdr(m2), avhdr0, buf, m3, false), 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 insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ bag ≠ ∅ → (bag -- n = ∅ ↔ bag = ∅ ++ n)

Rule argument

spec: bag-max name: bag-rem-empty seq: ⊦ bag ≠ ∅ → (bag -- n = ∅ ↔ bag = ∅ ++ n) subst: [n, bag] → [avhdr0.sqn, valid-sqns(v, m5, apebs)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%n < # apebs ⊦ apebs[n] = apeb ∧ valid-peb(v, m, apeb) → valid-sqns(v, m, apebs) ≠ ∅; (s)% ⊦ (∅ ++ n).max = n; (s) Used terms: avhdr0.sqn, valid-sqns(v, m5, apebs)