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Proof step 17 from proof valid-wl-use (previous step)

# apebs = # wlar, apebs[n] = mkpeb(aehdr1, avhdr1, buf1, m2, boolvar1), n < # wlar, valid-peb(v, m, mkpeb(aehdr0, avhdr0, buf0, m1, false)), valid-sqns(v, m, apebs) ≠ ∅ → valid-sqns(v, m, apebs).max < avhdr0.sqn, ∀ n. n < # wlar → (wlar[n].status = erroneous ↔ apebs[n].bad) ∧ (wlar[n].status = free → apebs[n].vidhdr = empty) ∧ (wlar[n].status ≠ erroneous ∧ wlar[n].status ≠ erasing → apebs[n].echdr = aechdr(wlar[n].ec)) ∧ (wlar[n].status = used → (∃ v, m. valid-peb(v, m, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m, apebs).max)), ∀ m0. m0 < # wlar ∧ m0 ≠ n ∧ wlar[m0].status = used → apebs[m0].vidhdr.vol ≠ v ∨ apebs[m0].vidhdr.leb ≠ m ⊦ avhdr0.sqn = valid-sqns(v, m, apebs[n, mkpeb(aehdr0, avhdr0, buf0, m1, false)]).max

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: sqns name: valid-sqns-write seq: ⊦ n < # apebs → valid-sqns(v, m, apebs[n, apeb]) = ( valid-sqns(v, m, apebs) \ (valid-peb(v, m, apebs[n]) ⊃ {apebs[n].vidhdr.sqn} ;∅)) ∪ (valid-peb(v, m, apeb) ⊃ {apeb.vidhdr.sqn} ;∅) subst: [apeb, n, apebs, m, v] → [mkpeb(aehdr0, avhdr0, buf0, m1, false), n, apebs, m, v] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ ¬ n < n; (s) Used terms: mkpeb(aehdr0, avhdr0, buf0, m1, false), n, apebs, m, v