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Proof step 15 from proof vols-is-max-is-max-vols (previous step)

# apebs = # wlar1, # wlar0 = # wlar1, avhdr.leb = VTBL_LNUM, avhdr.vol = VTBL_VOLID, wlar0[m0] = wl-entry(m3, used), apebs[m0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), m0 < # wlar1, bflipset-cons(bflipset0, wlar0), bflipset-cons(bflipset1, wlar1), is-encoded(to-vtbl(vols0), buf), unique-sqns(apebs), valid-ebatbl(apebs, wlar0, vols0, m0), valid-ebatbl(apebs, wlar1, vols1, m0), valid-eraseq(apebs, q0), valid-eraseq(wlar0, q0), valid-eraseq(q0), valid-eraseq(apebs, q1), valid-eraseq(wlar1, q1), valid-eraseq(q1), valid-eraseq-strong(apebs, to-vtbl(vols0), q0), valid-global-sqn(apebs, n1), valid-global-sqn(apebs, m1), valid-vtbl(apebs, vols1, wlar1, m0), valid-wl(apebs, wlar0), valid-wl(apebs, wlar1) ⊦ VTBL_VOLID ∈ vols0, VTBL_VOLID ∈ vols1, (v ∈ vols1 ↔ v ∈ vols0) ∧ (v ∈ vols1 → # vols1[v] = # vols0[v] ∧ (m < # vols1[v] ∧ vols1[v][m] ≠ unmapped → vols1[v][m] = vols0[v][m]))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ valid-vtbl(apebs, vols, wlar, n0) ↔ n0 < # apebs ∧ n0 < # wlar ∧ wlar[n0].status = used ∧ apebs[n0].vidhdr.vol = VTBL_VOLID ∧ apebs[n0].vidhdr.leb = VTBL_LNUM ∧ is-encoded(to-vtbl(vols), apebs[n0].data)
Proof step 17:
# wlar0 = # wlar1, # apebs = # wlar1, apebs[m0].vidhdr.leb = VTBL_LNUM, avhdr.leb = VTBL_LNUM, wlar1[m0].status = used, apebs[m0].vidhdr.vol = VTBL_VOLID, avhdr.vol = VTBL_VOLID, apebs[m0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), wlar0[m0] = wl-entry(m3, used), m0 < # apebs, m0 < # wlar1, bflipset-cons(bflipset1, wlar1), bflipset-cons(bflipset0, wlar0), is-encoded(to-vtbl(vols1), apebs[m0].data), is-encoded(to-vtbl(vols0), buf), unique-sqns(apebs), valid-ebatbl(apebs, wlar1, vols1, m0), valid-ebatbl(apebs, wlar0, vols0, m0), valid-eraseq(q1), valid-eraseq(wlar1, q1), valid-eraseq(apebs, q1), valid-eraseq(q0), valid-eraseq(wlar0, q0), valid-eraseq(apebs, q0), valid-eraseq-strong(apebs, to-vtbl(vols0), q0), valid-global-sqn(apebs, m1), valid-global-sqn(apebs, n1), valid-wl(apebs, wlar1), valid-wl(apebs, wlar0) ⊦ VTBL_VOLID ∈ vols1, VTBL_VOLID ∈ vols0, (v ∈ vols1 ↔ v ∈ vols0) ∧ (v ∈ vols1 → # vols1[v] = # vols0[v] ∧ (m < # vols1[v] ∧ vols1[v][m] ≠ unmapped → vols1[v][m] = vols0[v][m]))

Rule argument

spec: ubi-base name: valid-vtbl seq: ⊦ valid-vtbl(apebs, vols, wlar, n0) ↔ n0 < # apebs ∧ n0 < # wlar ∧ wlar[n0].status = used ∧ apebs[n0].vidhdr.vol = VTBL_VOLID ∧ apebs[n0].vidhdr.leb = VTBL_LNUM ∧ is-encoded(to-vtbl(vols), apebs[n0].data) subst: [n0, wlar, vols, apebs] → [m0, wlar1, vols1, apebs] flags: <all paths>

Additional information

Used terms: m0, wlar1, vols1, apebs