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Proof step 150 from proof refine-create (previous step)

cache_dirs[m1] = mkdir(m2, md1, # links(m1, cache_dirs), m5, 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), 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, ino = m ∨ ino ∈ cache_files ⊦ (ino = m ⊃ mkfile(0, md0, 1, ∅);(((cache_files ⊕ cache_pcache) ⊕ cache_icache) ++ m)[ino]) = mkfile (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 ] .inode .size, 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 ] .inode .meta, 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 ] .inode .nlink, (ino = m ⊃ mkfile(0, md0, 1, ∅);(cache_files ++ m)[ino]).content ⊕ mkcontent(ino, cache_pcache)), m = 0, 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 ] .inode .directory, str ∈ entries0, m ∈ cache_files, m ∈ cache_dirs

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 151:
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 ] .inode = mkinode(m0, md, boolvar, m3, m4, m6), cache_dirs[m1] = mkdir(m2, md1, # links(m1, cache_dirs), m5, entries0), ¬ boolvar, 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)) ], cache_sync → synced(cache_files, cache_icache, cache_pcache), ino = m ∨ ino ∈ cache_files, links(m1, cache_dirs) ≠ ∅ ∨ m1 = ROOT_INO ⊦ (ino = m ⊃ mkfile(0, md0, 1, ∅);(((cache_files ⊕ cache_pcache) ⊕ cache_icache) ++ m)[ino]) = mkfile(m6, md, m3, (ino = m ⊃ mkfile(0, md0, 1, ∅);(cache_files ++ m)[ino]).content ⊕ mkcontent(ino, cache_pcache)), m = 0, m ∈ cache_dirs, m ∈ cache_files, str ∈ entries0

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 [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 ] .inode, m0, md, boolvar, m3, m4, m6]

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 [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 ] .inode, m0, md, boolvar, m3, m4, m6