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Proof step 15 from proof valid-wl-erasing-invalidate (previous step)

# apebs = # wlar, avhdr1.sqn = valid-sqns(v, m1, apebs).max, apebs[n] = mkpeb(aechdr(m5), avhdr1, buf1, m4, false), wlar[n] = wl-entry(m5, used), wlar[m] = wl-entry(m0, erasing), m < # wlar, n < # wlar, valid-peb(v, m1, mkpeb(aechdr(m5), avhdr1, buf1, m4, false)) ⊦ avhdr1.sqn = valid-sqns(v, m1, apebs[m, mkpeb(aehdr, avhdr, buf, m2, false)]).max, n = m, valid-peb(mkpeb(aehdr, avhdr, buf, m2, false))

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(aehdr, avhdr, buf, m2, false), m, apebs, m1, 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(aehdr, avhdr, buf, m2, false), m, apebs, m1, v