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Proof step 194 from proof refine-link (previous step)

entries1[str] = entries2[str], cache_dirs[ino2] = mkdir(m7, md5, # links(ino2, cache_dirs), m11, entries1), entries[str] = entries2[str], cache_files[entries2[str]] = mkfile(m3, md6, # links(entries2[str], cache_dirs), content0), entries0[str] = entries2[str], cache_dirs[m9] = mkdir(m, md7, # links(m9, cache_dirs), m6, entries3), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries2[str]] = mkfile(m5, md1, # links(entries2[str], cache_dirs), content), cache_dirs[ino1] = mkdir(m0, md3, # links(ino1, cache_dirs), m2, entries0), cache_dirs[ino0] = mkdir(m4, md2, # links(ino0, cache_dirs), m10, entries), cache_dirs[ino3] = mkdir(m1, md4, # links(ino3, cache_dirs), m12, entries2), cache_icache[entries2[str]] = mkientry(boolvar0, mkinode(m8, md, true, m13, m14, m15)), 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), entries2[str] ∈ cache_files, str ∈ entries2, ino3 ∈ cache_dirs, str ∈ entries1, ino2 ∈ cache_dirs, ino0 ∈ cache_dirs, ino1 ∈ cache_dirs, str ∈ entries, str ∈ entries0, m9 ∈ cache_dirs, entries2[str] ∈ cache_icache, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(ino3, cache_dirs) ≠ ∅ ∨ ino3 = ROOT_INO, links(ino2, cache_dirs) ≠ ∅ ∨ ino2 = ROOT_INO, links(ino0, cache_dirs) ≠ ∅ ∨ ino0 = ROOT_INO, links(ino1, cache_dirs) ≠ ∅ ∨ ino1 = ROOT_INO, links(m9, cache_dirs) ≠ ∅ ∨ m9 = ROOT_INO ⊦ str0 ∈ entries3, (n ∈ content ↔ n ∈ content0 ⊕ mkcontent(entries2[str], cache_pcache)) ∧ (n ∈ content → content[n] = (content0 ⊕ mkcontent(entries2[str], cache_pcache))[n])

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: cache-base name: at-icache-overwrite-no-file seq: ⊦ ino ∈ icache ∧ icache[ino].inode.directory → (files ⊕ icache)[ino] = files[ino] subst: [ino, icache, files] → [entries2[str], cache_icache, cache_files ⊕ cache_pcache] flags: <all paths>

Additional information

Used simplifier rules: ⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache)); (s)%⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)% ⊦ mkientry(boolvar, inode).inode = inode; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkfile(m, md, m0, content).content = content; (s)%⊦ 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); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s) Used terms: entries2[str], cache_icache, cache_files ⊕ cache_pcache