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Proof step 28 from proof prepost-init-vols-mappings (previous step)

# wlar = # apebs, avhdr0.leb = VTBL_LNUM, avhdr0.vol = VTBL_VOLID, recs0[VTBL_VOLID × VTBL_LNUM] = recovery-entry(n0, m3), apebs[n] = mkpeb(aehdr, avhdr, buf, m, boolvar), apebs[n0] = mkpeb(aehdr0, avhdr0, buf0, m1, false), wlar[n0] = wl-entry(m4, used), avhdr0.valid?, n0 < # apebs, bflipset-cons(bflipset, wlar), unique-sqns(apebs), unmapped-vols(vols), valid-eraseq(wlar, q), valid-eraseq-stronger(apebs, q), valid-vtbl(apebs, vols, wlar, n), valid-wl(apebs, wlar), VTBL_VOLID × VTBL_LNUM ∈ recs0 ⊦ n0 = n, VTBL_VOLID ∈ vols, n ∈ q

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 29:
⊦ 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)
Proof step 30:
# wlar = # apebs, apebs[n].vidhdr.leb = VTBL_LNUM, avhdr0.leb = VTBL_LNUM, wlar[n].status = used, apebs[n].vidhdr.vol = VTBL_VOLID, avhdr0.vol = VTBL_VOLID, wlar[n0] = wl-entry(m4, used), apebs[n0] = mkpeb(aehdr0, avhdr0, buf0, m1, false), apebs[n] = mkpeb(aehdr, avhdr, buf, m, boolvar), recs0[VTBL_VOLID × VTBL_LNUM] = recovery-entry(n0, m3), avhdr0.valid?, n < # apebs, n < # wlar, n0 < # apebs, bflipset-cons(bflipset, wlar), is-encoded(to-vtbl(vols), apebs[n].data), unique-sqns(apebs), unmapped-vols(vols), valid-eraseq(wlar, q), valid-eraseq-stronger(apebs, q), valid-wl(apebs, wlar), VTBL_VOLID × VTBL_LNUM ∈ recs0 ⊦ n0 = n, n ∈ q, VTBL_VOLID ∈ vols

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 terms: n, wlar, vols, apebs