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Proof step 9 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(vtbl, buf), valid-recs(apebs, wlar, recs), valid-vtbl-weak(apebs, m0), VTBL_VOLID × VTBL_LNUM ∈ recs ⊦ unmapped-vols(∅)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ unmapped-vols(vols) ↔ (∀ v, m. v ∈ vols ∧ m < # vols[v] → vols[v][m] = unmapped)

Rule argument

spec: ubi-crash-recovery-base name: unmapped-vols seq: ⊦ unmapped-vols(vols) ↔ (∀ v, m. v ∈ vols ∧ m < # vols[v] → vols[v][m] = unmapped) subst: [vols] → [∅] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ¬ v ∈ ∅; (s) Used terms: ∅