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Proof step 51 from proof valid-wl-write-unmapped (previous step)

# apebs = # wlar, valid-sqns(VTBL_VOLID, VTBL_LNUM, apebs).max = valid-sqns(v, m, apebs).max, vols[v][m] = unmapped, wlar[n] = wl-entry(m5, erasing), wlar[n0] = wl-entry(m4, used), apebs[n0] = mkpeb(aechdr(m4), avidhdr(VTBL_VOLID, VTBL_LNUM, valid-sqns(v, m, apebs).max, m7, m3), buf0, m1, false), m < # vols[v], n < # wlar, n0 < # wlar, is-encoded(to-vtbl(vols), buf0), valid-peb(v, m, mkpeb(aechdr(m4), avidhdr(VTBL_VOLID, VTBL_LNUM, valid-sqns(v, m, apebs).max, m7, m3), buf0, m1, false)), valid-peb(mkpeb(aehdr, avhdr, buf, m0, boolvar)), valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)), v ∈ vols, m7 ≠ 0 → m7 ≤ datasize(buf0) ∧ m3 = checksum(buf0, m7) ⊦ valid-sqns(v, m, apebs).max = (valid-sqns(v, m, apebs) ++ avhdr.sqn).max, n0 = n, valid-peb(v, m, apebs[n]), VTBL_VOLID ∈ vols

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: valid-peb name: valid-peb2 seq: ⊦ valid-peb(v, m, apeb) ↔ ¬ apeb.bad ∧ apeb.echdr.valid? ∧ (∃ m0, m1, m2. apeb.vidhdr = avidhdr(v, m, m0, m1, m2) ∧ ( m1 ≠ 0 → m1 ≤ datasize(apeb.data) ∧ m2 = checksum(apeb.data, m1))) subst: [apeb, m, v] → [mkpeb (aechdr(m4), avidhdr (VTBL_VOLID, VTBL_LNUM, valid-sqns(v, m, apebs).max, m7, m3), buf0, m1, false), m, v] flags: <all paths>

Additional information

Used simplifier rules: ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)%⊦ avidhdr(v, m, m0, m1, m2) = avidhdr(v0, m3, m4, m5, m6) ↔ v = v0 ∧ m = m3 ∧ m0 = m4 ∧ m1 = m5 ∧ m2 = m6; (ws) Used terms: mkpeb (aechdr(m4), avidhdr(VTBL_VOLID, VTBL_LNUM, valid-sqns(v, m, apebs).max, m7, m3), buf0, m1, false), m, v