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Proof step 176 from proof refine-unlink (previous step)

# links(entries0[str], cache_dirs) = m0 + 1, cache_files[entries0[str]] = mkfile(m2, md3, m0 + 1, content), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str]] = mkfile(m7, md2, m0 + 1, content0), cache_dirs[m3] = mkdir(m9 + 1, md, # links(m3, cache_dirs), m4, entries0), afs-cons(cache_dirs[m3, mkdir(m9, md1, # links(m3, cache_dirs), m4, entries0 -- str)], cache_files[entries0[str], mkfile(m6, md0, m0, content)]), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), dcache-cons (cache_dcache -- dentrykey(m3, str), cache_dirs[m3, mkdir(m9, md1, # links(m3, cache_dirs), m4, entries0 -- str)], cache_files[entries0[str], mkfile(m6, md0, m0, content)]), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons (cache_icache[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m0, 0, m6))] [m3, mkientry(false, mkinode(m3, md1, true, # links(m3, cache_dirs), m4, m9)) ], cache_dirs[m3, mkdir(m9, md1, # links(m3, cache_dirs), m4, entries0 -- str)], cache_files[entries0[str], mkfile(m6, md0, m0, content)]), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons (cache_pcache, cache_dirs[m3, mkdir(m9, md1, # links(m3, cache_dirs), m4, entries0 -- str)], cache_files[entries0[str], mkfile(m6, md0, m0, content)]), pcache-cons(cache_pcache, cache_dirs, cache_files), synced (cache_dirs[m3, mkdir(m9, md1, # links(m3, cache_dirs), m4, entries0 -- str)], cache_icache[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m0, 0, m6))] [m3, mkientry(false, mkinode(m3, md1, true, # links(m3, cache_dirs), m4, m9)) ], cache_pcache), synced(cache_dirs, cache_icache, cache_pcache), ino ∈ cache_icache[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m0, 0, m6))] [m3, mkientry(false, mkinode(m3, md1, true, # links(m3, cache_dirs), m4, m9)) ], m3 ∈ cache_dirs, str ∈ entries0, entries0[str] ∈ cache_files, ino ∈ cache_files, cache_sync → synced (cache_files[entries0[str], mkfile(m6, md0, m0, content)], cache_icache[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m0, 0, m6))] [m3, mkientry(false, mkinode(m3, md1, true, # links(m3, cache_dirs), m4, m9)) ], cache_pcache), cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO ⊦ (ino = entries0[str] ⊃ mkfile(m6, md0, m0, content0);((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino]) = mkfile (cache_icache[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m0, 0, m6))] [m3, mkientry(false, mkinode(m3, md1, true, # links(m3, cache_dirs), m4, m9)) ] [ino ] .inode .size, cache_icache[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m0, 0, m6))] [m3, mkientry(false, mkinode(m3, md1, true, # links(m3, cache_dirs), m4, m9)) ] [ino ] .inode .meta, cache_icache[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m0, 0, m6))] [m3, mkientry(false, mkinode(m3, md1, true, # links(m3, cache_dirs), m4, m9)) ] [ino ] .inode .nlink, (ino = entries0[str] ⊃ mkfile(m6, md0, m0, content);cache_files[ino]).content ⊕ mkcontent(ino, cache_pcache)), cache_icache[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m0, 0, m6))] [m3, mkientry(false, mkinode(m3, md1, true, # links(m3, cache_dirs), m4, m9)) ] [ino ] .inode .directory

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 177:
# links(entries0[str], cache_dirs) = m0 + 1, cache_icache[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m0, 0, m6))] [m3, mkientry(false, mkinode(m3, md1, true, # links(m3, cache_dirs), m4, m9)) ] [ino ] .inode = mkinode(m, md4, boolvar, m1, m5, m8), cache_dirs[m3] = mkdir(m9 + 1, md, # links(m3, cache_dirs), m4, entries0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str]] = mkfile(m7, md2, m0 + 1, content0), cache_files[entries0[str]] = mkfile(m2, md3, m0 + 1, content), ¬ boolvar, afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs[m3, mkdir(m9, md1, # links(m3, cache_dirs), m4, entries0 -- str)], cache_files[entries0[str], mkfile(m6, md0, m0, content)]), dcache-cons(cache_dcache, cache_dirs, cache_files), dcache-cons (cache_dcache -- dentrykey(m3, str), cache_dirs[m3, mkdir(m9, md1, # links(m3, cache_dirs), m4, entries0 -- str)], cache_files[entries0[str], mkfile(m6, md0, m0, content)]), icache-cons(cache_icache, cache_dirs, cache_files), icache-cons (cache_icache[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m0, 0, m6))] [m3, mkientry(false, mkinode(m3, md1, true, # links(m3, cache_dirs), m4, m9)) ], cache_dirs[m3, mkdir(m9, md1, # links(m3, cache_dirs), m4, entries0 -- str)], cache_files[entries0[str], mkfile(m6, md0, m0, content)]), pcache-cons(cache_pcache, cache_dirs, cache_files), pcache-cons (cache_pcache, cache_dirs[m3, mkdir(m9, md1, # links(m3, cache_dirs), m4, entries0 -- str)], cache_files[entries0[str], mkfile(m6, md0, m0, content)]), synced(cache_dirs, cache_icache, cache_pcache), synced (cache_dirs[m3, mkdir(m9, md1, # links(m3, cache_dirs), m4, entries0 -- str)], cache_icache[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m0, 0, m6))] [m3, mkientry(false, mkinode(m3, md1, true, # links(m3, cache_dirs), m4, m9)) ], cache_pcache), ino ∈ cache_files, entries0[str] ∈ cache_files, str ∈ entries0, m3 ∈ cache_dirs, ino ∈ cache_icache[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m0, 0, m6))] [m3, mkientry(false, mkinode(m3, md1, true, # links(m3, cache_dirs), m4, m9)) ], cache_sync → synced(cache_files, cache_icache, cache_pcache), cache_sync → synced (cache_files[entries0[str], mkfile(m6, md0, m0, content)], cache_icache[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m0, 0, m6))] [m3, mkientry(false, mkinode(m3, md1, true, # links(m3, cache_dirs), m4, m9)) ], cache_pcache), links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO ⊦ (ino = entries0[str] ⊃ mkfile(m6, md0, m0, content0);((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino]) = mkfile(m8, md4, m1, (ino = entries0[str] ⊃ mkfile(m6, md0, m0, content);cache_files[ino]).content ⊕ mkcontent(ino, cache_pcache))

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [cache_icache [entries0[str], mkientry (false, mkinode(entries0[str], md0, false, m0, 0, m6)) ] [m3, mkientry (false, mkinode (m3, md1, true, # links(m3, cache_dirs), m4, m9)) ] [ino ] .inode, m, md4, boolvar, m1, m5, m8]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: cache_icache [entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m0, 0, m6)) ] [m3, mkientry (false, mkinode(m3, md1, true, # links(m3, cache_dirs), m4, m9)) ] [ino ] .inode, m, md4, boolvar, m1, m5, m8