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Proof step 43 from proof refine-evict (previous step)

# links(m, cache_dirs) = 0, cache_icache[ino].inode = mkinode(m1, md, boolvar, m3, m4, m5), cache_dirs[m] = mkdir(m0, md0, 0, m2, entries), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), m ∈ cache_dirs, ino ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino] = ((cache_files ⊕ cache_pcache) ⊕ (cache_icache -- m))[ino], ino = m, m = ROOT_INO, ¬ boolvar ∧ ino ∈ cache_icache

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 44:
# links(m, cache_dirs) = 0, cache_dirs[m] = mkdir(m0, md0, 0, m2, entries), cache_icache[ino] = mkientry(boolvar0, inode), inode = mkinode(m1, md, boolvar, m3, m4, m5), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), ino ∈ cache_files, m ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino] = ((cache_files ⊕ cache_pcache) ⊕ (cache_icache -- m))[ino], ino = m, m = ROOT_INO, ¬ boolvar ∧ ino ∈ cache_icache

Rule argument

spec: icache-entry name: elim seq: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode) subst: [ie, boolvar, inode] → [cache_icache[ino], boolvar0, inode]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode); (elim) Used terms: cache_icache[ino], boolvar0, inode