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Proof step 129 from proof refine-create (previous step)

cache_icache[m1, mkientry(false, mkinode(m1, md2, true, # links(m1, cache_dirs), m5, m2 + 1))][ino] = mkientry(boolvar0, mkinode(m0, md, true, m3, m4, m6)), cache_dirs[m1] = mkdir(m2, md1, # links(m1, cache_dirs), m5, entries0), cache_files[ino] = mkfile(m7, md3, # links(ino, cache_dirs), 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), ino ∈ cache_files, ino ∈ cache_icache[m1, mkientry(false, mkinode(m1, md2, true, # links(m1, cache_dirs), m5, m2 + 1))] [m, mkientry(false, mkinode(m, md0, false, 1, 0, 0)) ], m1 ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m1, cache_dirs) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino] = mkfile(m7, md3, # links(ino, cache_dirs), content ⊕ mkcontent(ino, cache_pcache)), m = 0, str ∈ entries0, m ∈ cache_files, m ∈ cache_dirs

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 130:
⊦ 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 131:
cache_files[ino] = mkfile(m7, md3, # links(ino, cache_dirs), content), cache_dirs[m1] = mkdir(m2, md1, # links(m1, cache_dirs), m5, entries0), cache_icache[m1, mkientry(false, mkinode(m1, md2, true, # links(m1, cache_dirs), m5, m2 + 1))][ino] = mkientry(boolvar0, mkinode(m0, md, true, m3, m4, m6)), 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), m1 ∈ cache_dirs, ino ∈ cache_icache[m1, mkientry(false, mkinode(m1, md2, true, # links(m1, cache_dirs), m5, m2 + 1))] [m, mkientry(false, mkinode(m, md0, false, 1, 0, 0)) ], ino ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m1, cache_dirs) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino] = mkfile(m7, md3, # links(ino, cache_dirs), content ⊕ mkcontent(ino, cache_pcache)), m = 0, m ∈ cache_dirs, m ∈ cache_files, str ∈ entries0, ino ∈ cache_icache ∧ ¬ cache_icache[ino].inode.directory
Proof step 139:
cache_files[ino] = mkfile(m7, md3, # links(ino, cache_dirs), content), cache_dirs[m1] = mkdir(m2, md1, # links(m1, cache_dirs), m5, entries0), cache_icache[m1, mkientry(false, mkinode(m1, md2, true, # links(m1, cache_dirs), m5, m2 + 1))][ino] = mkientry(boolvar0, mkinode(m0, md, true, m3, m4, m6)), 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), m1 ∈ cache_dirs, ino ∈ cache_icache[m1, mkientry(false, mkinode(m1, md2, true, # links(m1, cache_dirs), m5, m2 + 1))] [m, mkientry(false, mkinode(m, md0, false, 1, 0, 0)) ], ino ∈ cache_files, ino ∈ cache_icache, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m1, cache_dirs) ≠ ∅ ∨ m1 = ROOT_INO ⊦ m = 0, mkfile(cache_icache[ino].inode.size, cache_icache[ino].inode.meta, cache_icache[ino].inode.nlink, (cache_files ⊕ cache_pcache)[ino].content) = mkfile(m7, md3, # links(ino, cache_dirs), content ⊕ mkcontent(ino, cache_pcache)), cache_icache[ino].inode.directory, m ∈ cache_dirs, m ∈ cache_files, str ∈ entries0

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] → [ino, cache_icache, cache_files ⊕ cache_pcache] flags: <all paths>

Additional information

Used terms: ino, cache_icache, cache_files ⊕ cache_pcache