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Proof step 34 from proof absexpt-id-apebs-used (previous step)

# vols[v0] = # avols[v0], # wlar = # apebs, wlar[n] = wl-entry(m0, stat), apebs[n] = mkpeb(aehdr0, avhdr0, buf0, m4, boolvar0), vols[v0][m1] = ⌜n⌝ , avols[v0][m1] = mapped(buf0, m3), m1 < # avols[v0], n < # apebs, valid-ebatbl(apebs, wlar, vols, n0), v0 ∈ avols, v0 ∈ vols, m4 ≤ m3, v0 ≠ v ∨ m1 ≠ m ⊦ stat = used, buf0 = buf ∧ m2 ≤ m3

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 35:
⊦ 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 36:
# wlar = # apebs, # vols[v0] = # avols[v0], avols[v0][m1] = mapped(buf0, m3), vols[v0][m1] = ⌜n⌝ , apebs[n] = mkpeb(aehdr0, avhdr0, buf0, m4, boolvar0), wlar[n] = wl-entry(m0, stat), n < # apebs, m1 < # avols[v0], v0 ∈ vols, v0 ∈ avols, m4 ≤ m3, ∀ 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, v0 ≠ v ∨ m1 ≠ m ⊦ stat = used, buf0 = buf ∧ m2 ≤ m3

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