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Proof step 175 from proof refine-mkdir (previous step)

cache_dirs[m1] = mkdir(m6, md1, # links(m1, cache_dirs), m8, entries1), (cache_dirs[m1, mkdir(m6 + 1, md1, # links(m1, cache_dirs), m8 + 1, entries1[str, m5])] ++ m5)[m1] = mkdir(m, md0, m3, m4, entries0), (∅)[ino] = mkientry(boolvar1, mkinode(m11, md5, false, m12, m13, m14)), cache_files[ino] = mkfile(m10, md4, # links(ino, cache_dirs), content), 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), ino ∈ cache_files, m1 ∈ cache_dirs, ino ∈ cache_icache[m1, mkientry(false, mkinode(m1, md2, true, m3, m4, m))][m5, mkientry(false, mkinode(m5, md3, true, 1, 0, 0))], cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m1, cache_dirs) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ino = m1, m5 = 0, str ∈ entries1, m5 ∈ cache_files, m5 ∈ cache_dirs, ino ∈ cache_icache, m10 = m14 ∧ md4 = md5 ∧ # links(ino, cache_dirs) = m12

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: store, inst: icache name: In-insert seq: ⊦ ino ∈ icache[ino0, ie] ↔ ino = ino0 ∨ ino ∈ icache subst: [ino, icache, ino0, ie] → [ino, cache_icache [m1, mkientry(false, mkinode(m1, md2, true, m3, m4, m)) ], m5, mkientry(false, mkinode(m5, md3, true, 1, 0, 0))] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ino ≠ ino0 → (ino ∈ icache[ino0, ie] ↔ ino ∈ icache); (s) Used terms: ino, cache_icache[m1, mkientry(false, mkinode(m1, md2, true, m3, m4, m))], m5, mkientry(false, mkinode(m5, md3, true, 1, 0, 0))