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Proof step 22 from proof valid-wl-write-unmapped (previous step)

# apebs = # wlar, avhdr1.sqn = valid-sqns(VTBL_VOLID, VTBL_LNUM, apebs).max, avhdr0.sqn = valid-sqns(v, m, apebs).max, apebs[n1] = mkpeb(aechdr(m4), avhdr0, buf0, m1, false), wlar[n0] = wl-entry(m6, used), wlar[n] = wl-entry(m5, erasing), wlar[n1] = wl-entry(m4, used), vols[avhdr.vol][avhdr.leb] = unmapped, apebs[n0] = mkpeb(aechdr(m6), avhdr1, buf1, m2, false), n < # wlar, avhdr.leb < # vols[avhdr.vol], n0 < # wlar, n1 < # wlar, is-encoded(to-vtbl(vols), buf1), valid-peb(VTBL_VOLID, VTBL_LNUM, mkpeb(aechdr(m6), avhdr1, buf1, m2, false)), valid-peb(mkpeb(aehdr, avhdr, buf, m0, boolvar)), valid-peb(v, m, mkpeb(aechdr(m4), avhdr0, buf0, m1, false)), avhdr.vol ∈ vols, ∀ v, m, n2. vols[v][m] = ⌜n2⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n2].status = used ∧ n2 < # wlar ∧ apebs[n2].vidhdr.valid? ∧ apebs[n2].vidhdr.vol = v ∧ apebs[n2].vidhdr.leb = m ∧ n2 ≠ n0 ⊦ avhdr0.sqn = valid-sqns(v, m, apebs[n, mkpeb(aehdr, avhdr, buf, m0, boolvar)]).max, n1 = n, VTBL_VOLID ∈ vols

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, m0, boolvar), 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(aehdr, avhdr, buf, m0, boolvar), n, apebs, m, v