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Proof step 11 from proof lf-mapped-valid-peb (previous step)

avhdr.sqn = valid-sqns(v0, m1, apebs).max, apebs[n] = mkpeb(aechdr(m0), avhdr, buf, m2, false), wlar[n] = wl-entry(m0, used), vols[v][m] = ⌜n⌝ , m < # vols[v], n < # wlar, valid-ebatbl(apebs, wlar, vols, n0), valid-peb(v0, m1, mkpeb(aechdr(m0), avhdr, buf, m2, false)), v ∈ vols ⊦ n = n0, v0 = v ∧ m1 = m

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ valid-ebatbl(apebs, wlar, vols, n0) ↔ (∀ v, m, n. vols[v][m] = ⌜n⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n].status = used ∧ n < # apebs ∧ n < # wlar ∧ apebs[n].vidhdr.valid? ∧ apebs[n].vidhdr.vol = v ∧ apebs[n].vidhdr.leb = m ∧ n ≠ n0)
Proof step 13:
avhdr.sqn = valid-sqns(v0, m1, apebs).max, vols[v][m] = ⌜n⌝ , wlar[n] = wl-entry(m0, used), apebs[n] = mkpeb(aechdr(m0), avhdr, buf, m2, false), n < # wlar, m < # vols[v], valid-peb(v0, m1, mkpeb(aechdr(m0), avhdr, buf, m2, false)), v ∈ vols, ∀ v, m, n. vols[v][m] = ⌜n⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n].status = used ∧ n < # apebs ∧ n < # wlar ∧ apebs[n].vidhdr.valid? ∧ apebs[n].vidhdr.vol = v ∧ apebs[n].vidhdr.leb = m ∧ n ≠ n0 ⊦ n = n0, v0 = v ∧ m1 = m

Rule argument

spec: ubi-base name: valid-ebatbl seq: ⊦ valid-ebatbl(apebs, wlar, vols, n0) ↔ (∀ v, m, n. vols[v][m] = ⌜n⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n].status = used ∧ n < # apebs ∧ n < # wlar ∧ apebs[n].vidhdr.valid? ∧ apebs[n].vidhdr.vol = v ∧ apebs[n].vidhdr.leb = m ∧ n ≠ n0) subst: [n0, vols, wlar, apebs] → [n0, vols, wlar, apebs] flags: <all paths>

Additional information

Used terms: n0, vols, wlar, apebs