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Proof step 33 from proof prepost-init-vols-sizes (previous step)

# apebs = # wlar, recs[VTBL_VOLID × VTBL_LNUM] = recovery-entry(m0, m1), apebs[m0] = mkpeb(aehdr, avhdr, buf, m, boolvar), m0 < # wlar, is-encoded(to-vtbl(vols), buf), unmapped-vols(vols), valid-recs(apebs, wlar, recs), valid-vtbl-weak(apebs, m0), VTBL_VOLID × VTBL_LNUM ∈ recs ⊦ valid-vtbl(apebs, vols, wlar, m0) ∧ ¬ VTBL_VOLID ∈ vols

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 34:
⊦ 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 35:
# apebs = # wlar, apebs[m0] = mkpeb(aehdr, avhdr, buf, m, boolvar), recs[VTBL_VOLID × VTBL_LNUM] = recovery-entry(m0, m1), m0 < # wlar, is-encoded(to-vtbl(vols), buf), unmapped-vols(vols), valid-recs(apebs, wlar, recs), valid-vtbl-weak(apebs, m0), VTBL_VOLID × VTBL_LNUM ∈ recs ⊦ ( m0 < # apebs ∧ m0 < # wlar ∧ wlar[m0].status = used ∧ apebs[m0].vidhdr.vol = VTBL_VOLID ∧ apebs[m0].vidhdr.leb = VTBL_LNUM ∧ is-encoded(to-vtbl(vols), apebs[m0].data)) ∧ ¬ VTBL_VOLID ∈ vols

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, wlar, vols, apebs] flags: <all paths>

Additional information

Used terms: m0, wlar, vols, apebs