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Proof step 3 from proof lf-mapped-valid-vidhdr (previous step)

apebs[n] = mkpeb(aehdr, avhdr, buf, m0, boolvar), vols[v][m] = ⌜n⌝ , m < # vols[v], n < # apebs, valid-ebatbl(apebs, wlar, vols, n0), v ∈ vols ⊦ avhdr.valid?

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ 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 5:
vols[v][m] = ⌜n⌝ , apebs[n] = mkpeb(aehdr, avhdr, buf, m0, boolvar), n < # apebs, m < # vols[v], 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 ⊦ avhdr.valid?

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