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Proof step 15 from proof lf-valid-eraseq-stronger-notin-recs (previous step)

# apebs = # wlar, avhdr.sqn = valid-sqns(v0, m1, apebs).max, wlar[n] = wl-entry(m2, used), apebs[n] = mkpeb(aechdr(m2), avhdr, buf, m0, false), n < # wlar, valid-eraseq(wlar, q), valid-eraseq-stronger(apebs, q), valid-peb(v0, m1, mkpeb(aechdr(m2), avhdr, buf, m0, false)), valid-recs(apebs, wlar, recs) ⊦ avhdr = empty, n ∈ q, v0 × m1 ∈ recs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ valid-recs(apebs, wlar, recs) ↔ (∀ ladr, m. ladr ∈ recs ∧ recs[ladr].pnum = m ↔ wlar[m].status = used ∧ m < # apebs ∧ apebs[m].vidhdr.vol = ladr.vol ∧ apebs[m].vidhdr.leb = ladr.leb)
Proof step 17:
# apebs = # wlar, avhdr.sqn = valid-sqns(v0, m1, apebs).max, apebs[n] = mkpeb(aechdr(m2), avhdr, buf, m0, false), wlar[n] = wl-entry(m2, used), n < # wlar, valid-eraseq(wlar, q), valid-eraseq-stronger(apebs, q), valid-peb(v0, m1, mkpeb(aechdr(m2), avhdr, buf, m0, false)), ∀ ladr, m. ladr ∈ recs ∧ recs[ladr].pnum = m ↔ wlar[m].status = used ∧ m < # apebs ∧ apebs[m].vidhdr.vol = ladr.vol ∧ apebs[m].vidhdr.leb = ladr.leb ⊦ avhdr = empty, v0 × m1 ∈ recs, n ∈ q

Rule argument

spec: ubi-crash-recovery-base name: valid-recs seq: ⊦ valid-recs(apebs, wlar, recs) ↔ (∀ ladr, m. ladr ∈ recs ∧ recs[ladr].pnum = m ↔ wlar[m].status = used ∧ m < # apebs ∧ apebs[m].vidhdr.vol = ladr.vol ∧ apebs[m].vidhdr.leb = ladr.leb) subst: [recs, wlar, apebs] → [recs, wlar, apebs] flags: <all paths>

Additional information

Used terms: recs, wlar, apebs