[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 24 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), m2 < # vols[v0], m0 < # wlar, is-encoded(to-vtbl(vols) ∪ vtbl0, buf), unmapped-vols(vols), valid-recs(apebs, wlar, recs), valid-vtbl-weak(apebs, m0), v0 ∈ vols, v ∈ vtbl0, VTBL_VOLID × VTBL_LNUM ∈ recs, to-vtbl(vols) ⊥ vtbl0 ⊦ vols[v0][m2] = unmapped, vtbl0 = ∅, v ∈ vols

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ unmapped-vols(vols) ↔ (∀ v, m. v ∈ vols ∧ m < # vols[v] → vols[v][m] = unmapped)
Proof step 26:
# apebs = # wlar, apebs[m0] = mkpeb(aehdr, avhdr, buf, m, boolvar), recs[VTBL_VOLID × VTBL_LNUM] = recovery-entry(m0, m1), m0 < # wlar, m2 < # vols[v0], is-encoded(to-vtbl(vols) ∪ vtbl0, buf), valid-recs(apebs, wlar, recs), valid-vtbl-weak(apebs, m0), VTBL_VOLID × VTBL_LNUM ∈ recs, v ∈ vtbl0, v0 ∈ vols, to-vtbl(vols) ⊥ vtbl0, ∀ v, m. v ∈ vols ∧ m < # vols[v] → vols[v][m] = unmapped ⊦ vols[v0][m2] = unmapped, vtbl0 = ∅, v ∈ vols

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] → [vols] flags: <all paths>

Additional information

Used terms: vols