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Proof step 28 from proof prepost-init-vols-sizes (previous step)

# 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) ∪ vtbl, buf), unmapped-vols(vols), valid-recs(apebs, wlar, recs), valid-vtbl-weak(apebs, m0), VTBL_VOLID × VTBL_LNUM ∈ recs, to-vtbl(vols) ⊥ vtbl ⊦ vtbl = ∅, ∃ v. v ∈ vtbl

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 29:
⊦ vtbl = vtbl0 ↔ (∀ v. (v ∈ vtbl ↔ v ∈ vtbl0) ∧ vtbl[v] = vtbl0[v])
Proof step 30:
# 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) ∪ vtbl, buf), unmapped-vols(vols), valid-recs(apebs, wlar, recs), valid-vtbl-weak(apebs, m0), VTBL_VOLID × VTBL_LNUM ∈ recs, to-vtbl(vols) ⊥ vtbl ⊦ ∀ v. (v ∈ vtbl ↔ v ∈ ∅) ∧ vtbl[v] = (∅)[v], ∃ v. v ∈ vtbl

Rule argument

spec: store, inst: vtbl name: Extension seq: ⊦ vtbl = vtbl0 ↔ (∀ v. (v ∈ vtbl ↔ v ∈ vtbl0) ∧ vtbl[v] = vtbl0[v]) subst: [vtbl0, vtbl] → [∅, vtbl] flags: <all paths>

Additional information

Used terms: ∅, vtbl