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Proof step 157 from proof prepost-init-vols-mappings (previous step)

# wlar0 = # wlar, # apebs = # wlar, apebs[n] = mkpeb(aehdr, avhdr, buf, m, boolvar), bflipset-cons(bflipset0, wlar0), bflipset-cons(bflipset, wlar), is-encoded(vtbl, buf), unique-sqns(apebs), unmapped-vols(vols0), valid-eraseq(wlar0, q1), valid-eraseq(wlar, q), valid-eraseq-strong(apebs, vtbl, q), valid-eraseq-stronger(apebs, q1), valid-recs(apebs, wlar0, recs0), valid-vtbl(apebs, vols0, wlar0, n), valid-vtbl(apebs, vols, wlar, n), valid-wl(apebs, wlar0), valid-wl(apebs, wlar), q1 ⊆ q, ∅ ⊥ vols, ∀ v, m0, n0. v ∈ vols ∧ m0 < # vols[v] ∧ vols[v][m0] = ⌜n0⌝ ↔ wlar[n0].status = used ∧ n0 < # wlar ∧ apebs[n0].vidhdr.valid? ∧ apebs[n0].vidhdr.vol = v ∧ apebs[n0].vidhdr.leb = m0 ∧ n0 ≠ n ⊦ valid-ebatbl(apebs, wlar, vols, n), n ∈ q1, VTBL_VOLID ∈ vols0, VTBL_VOLID ∈ vols

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 158:
⊦ 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 159:
# apebs = # wlar, # wlar0 = # wlar, apebs[n] = mkpeb(aehdr, avhdr, buf, m, boolvar), bflipset-cons(bflipset, wlar), bflipset-cons(bflipset0, wlar0), is-encoded(vtbl, buf), unique-sqns(apebs), unmapped-vols(vols0), valid-eraseq(wlar, q), valid-eraseq(wlar0, q1), valid-eraseq-strong(apebs, vtbl, q), valid-eraseq-stronger(apebs, q1), valid-recs(apebs, wlar0, recs0), valid-vtbl(apebs, vols, wlar, n), valid-vtbl(apebs, vols0, wlar0, n), valid-wl(apebs, wlar), valid-wl(apebs, wlar0), q1 ⊆ q, ∅ ⊥ vols, ∀ v, m0, n0. v ∈ vols ∧ m0 < # vols[v] ∧ vols[v][m0] = ⌜n0⌝ ↔ wlar[n0].status = used ∧ n0 < # wlar ∧ apebs[n0].vidhdr.valid? ∧ apebs[n0].vidhdr.vol = v ∧ apebs[n0].vidhdr.leb = m0 ∧ n0 ≠ n ⊦ VTBL_VOLID ∈ vols, VTBL_VOLID ∈ vols0, n ∈ q1, ∀ v, m, n1. vols[v][m] = ⌜n1⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n1].status = used ∧ n1 < # apebs ∧ n1 < # wlar ∧ apebs[n1].vidhdr.valid? ∧ apebs[n1].vidhdr.vol = v ∧ apebs[n1].vidhdr.leb = m ∧ n1 ≠ n

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] → [n, vols, wlar, apebs] flags: <all paths>

Additional information

Used terms: n, vols, wlar, apebs