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Proof step 414 from proof refine-rename-file-negdentry (previous step)

cache_dirs[m3] = mkdir(m0, md4, # links(m3, cache_dirs), m2, entries0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str]] = mkfile(m9, md2, m11, content), cache_dirs[m] = mkdir(m8, md3, # links(m, cache_dirs), m13, entries), cache_files[entries0[str]] = mkfile(m1, md1, # links(entries0[str], cache_dirs), content0), 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), str ∈ entries0, m3 ∈ cache_dirs, entries0[str] ∈ cache_files, m ∈ cache_dirs, m = m3 → md = md0, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ m11 = # links(entries0[str], cache_dirs), str0 ∈ entries

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 415:
⊦ ino ∈ icache ∧ ¬ icache[ino].inode.directory → (files ⊕ icache)[ino] = mkfile(icache[ino].inode.size, icache[ino].inode.meta, icache[ino].inode.nlink, files[ino].content)
Proof step 416:
cache_files[entries0[str]] = mkfile(m1, md1, # links(entries0[str], cache_dirs), content0), cache_dirs[m] = mkdir(m8, md3, # links(m, cache_dirs), m13, entries), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str]] = mkfile(m9, md2, m11, content), cache_dirs[m3] = mkdir(m0, md4, # links(m3, cache_dirs), m2, entries0), 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), m ∈ cache_dirs, entries0[str] ∈ cache_files, m3 ∈ cache_dirs, str ∈ entries0, cache_sync → synced(cache_files, cache_icache, cache_pcache), m = m3 → md = md0, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO, links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO ⊦ m11 = # links(entries0[str], cache_dirs), str0 ∈ entries, entries0[str] ∈ cache_icache ∧ ¬ cache_icache[entries0[str]].inode.directory
Proof step 423:
cache_files[entries0[str]] = mkfile(m1, md1, # links(entries0[str], cache_dirs), content0), cache_dirs[m] = mkdir(m8, md3, # links(m, cache_dirs), m13, entries), cache_dirs[m3] = mkdir(m0, md4, # links(m3, cache_dirs), m2, entries0), mkfile (cache_icache[entries0[str]].inode.size, cache_icache[entries0[str]].inode.meta, cache_icache[entries0[str]].inode.nlink, (cache_files ⊕ cache_pcache)[entries0[str]].content) = mkfile(m9, md2, m11, content), 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), m ∈ cache_dirs, entries0[str] ∈ cache_files, m3 ∈ cache_dirs, str ∈ entries0, entries0[str] ∈ cache_icache, cache_sync → synced(cache_files, cache_icache, cache_pcache), m = m3 → md = md0, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO, links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO ⊦ m11 = # links(entries0[str], cache_dirs), cache_icache[entries0[str]].inode.directory, str0 ∈ entries

Rule argument

spec: cache-base name: at-icache-overwrite seq: ⊦ ino ∈ icache ∧ ¬ icache[ino].inode.directory → (files ⊕ icache)[ino] = mkfile (icache[ino].inode.size, icache[ino].inode.meta, icache[ino].inode.nlink, files[ino].content) subst: [ino, icache, files] → [entries0[str], cache_icache, cache_files ⊕ cache_pcache] flags: <all paths>

Additional information

Used terms: entries0[str], cache_icache, cache_files ⊕ cache_pcache