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Proof step 12 from proof prepost-init-vols-mappings (previous step)

# wlar = # apebs, wlar[n0] = wl-entry(m4, stat), apebs[n0] = mkpeb(aehdr0, avhdr0, buf0, m1, boolvar0), apebs[n] = mkpeb(aehdr, avhdr, buf, m, boolvar), recs0[v × m0] = recovery-entry(m2, m3), bflipset-cons(bflipset, wlar), unique-sqns(apebs), unmapped-vols(vols), valid-eraseq(wlar, q), valid-eraseq-stronger(apebs, q), valid-recs(apebs, wlar, recs0), valid-vtbl(apebs, vols, wlar, n), valid-wl(apebs, wlar) ⊦ n ∈ q, VTBL_VOLID ∈ vols, ∃ vtbl. is-encoded(vtbl, buf)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: ubi-base name: valid-vtbl seq: ⊦ valid-vtbl(apebs, vols, wlar, n0) ↔ n0 < # apebs ∧ n0 < # wlar ∧ wlar[n0].status = used ∧ apebs[n0].vidhdr.vol = VTBL_VOLID ∧ apebs[n0].vidhdr.leb = VTBL_LNUM ∧ is-encoded(to-vtbl(vols), apebs[n0].data) subst: [n0, wlar, vols, apebs] → [n, wlar, vols, apebs] flags: <all paths>

Additional information

Used simplifier rules: f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ m < n → n ≠ 0; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).data = buf; (s)% ⊦ is-encoded(vtbl0, buf) → (is-encoded(vtbl1, buf) ↔ vtbl0 = vtbl1); (s) Used terms: n, wlar, vols, apebs