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Proof step 24 from proof abs-idset-fwd (previous step)

# vols[v] = # avols[v], # apebs1 = # apebs0, apebs0[m3] = mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0), apebs1[m3] = mkpeb(aehdr, avhdr, buf, m0, boolvar), avols[v][m] = mapped(buf0, m1), vols[v][m] = ⌜m3⌝ , m < # avols[v], valid-ebatbl(apebs0, wlar, vols, n0), v ∈ vols, v ∈ avols, m2 ≤ m1, # apebs0 ≤ m3 ⊦ buf0 = buf ∧ m0 ≤ m1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ 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 26:
# apebs1 = # apebs0, # vols[v] = # avols[v], vols[v][m] = ⌜m3⌝ , avols[v][m] = mapped(buf0, m1), apebs1[m3] = mkpeb(aehdr, avhdr, buf, m0, boolvar), apebs0[m3] = mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0), m < # avols[v], v ∈ avols, v ∈ vols, # apebs0 ≤ m3, m2 ≤ m1, ∀ v, m, n. vols[v][m] = ⌜n⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n].status = used ∧ n < # apebs0 ∧ n < # wlar ∧ apebs0[n].vidhdr.valid? ∧ apebs0[n].vidhdr.vol = v ∧ apebs0[n].vidhdr.leb = m ∧ n ≠ n0 ⊦ buf0 = buf ∧ m0 ≤ m1

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, apebs0] flags: <all paths>

Additional information

Used terms: n0, vols, wlar, apebs0