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Proof step 100 from proof refine-mkdir (previous step)

(cache_dirs[m1, mkdir(m6 + 1, md1, # links(m1, cache_dirs), m8 + 1, entries1[str, m5])] ++ m5)[m1] = mkdir(m, md0, m3, m4, entries0), cache_dirs[m1] = mkdir(m6, md1, # links(m1, cache_dirs), m8, entries1), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, dirs = (cache_dirs[m1, mkdir(m6 + 1, md1, # links(m1, cache_dirs), m8 + 1, entries1[str, m5])] ++ m5)[m5, mkdir(0, md3, 1, 0, ∅)], m5 ≠ 0, 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), m1 ∈ cache_dirs, ¬ str ∈ entries1, ¬ m5 ∈ cache_files, ¬ m5 ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m1, cache_dirs) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ⟨afs_inode_sync#(mkinode(m1, md2, true, # links(m1, cache_dirs), m8, m6); dirs, afs_files); p_inode := (m1 ∈ dirs ⊃ mkinode(m1, dirs[m1].meta, true, dirs[m1].nlink, dirs[m1].nsubdirs, dirs[m1].size) ;mkinode(m1, afs_files[m1].meta, false, afs_files[m1].nlink, 0, afs_files[m1].size) ); c_inode := getinode(mkdentry(str, m5).ino, dirs, afs_files); asynced := ?⟩ ( dirs = (cache_dirs[m1, mkdir(m6 + 1, md1, # links(m1, cache_dirs), m8 + 1, entries1[str, m5])] ++ m5)[m5, mkdir(0, md3, 1, 0, ∅)] [m1, mkdir(m, md2, m3, m4, entries0) ] ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache[m1, mkientry(false, mkinode(m1, md2, true, m3, m4, m))][m5, mkientry(false, mkinode(m5, md3, true, 1, 0, 0))] ∧ (asynced ↔ asynced0) ∧ mkinode(m1, md2, true, m3, m4, m) = p_inode ∧ mkinode(m5, md3, true, 1, 0, 0) = c_inode)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 101:
cache_dirs[m1] = mkdir(m6, md1, # links(m1, cache_dirs), m8, entries1), (cache_dirs[m1, mkdir(m6 + 1, md1, # links(m1, cache_dirs), m8 + 1, entries1[str, m5])] ++ m5)[m1] = mkdir(m, md0, m3, m4, entries0), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, dirs = (cache_dirs[m1, mkdir(m6 + 1, md1, # links(m1, cache_dirs), m8 + 1, entries1[str, m5])] ++ m5)[m5, mkdir(0, md3, 1, 0, ∅)], files = afs_files, inode = mkinode(m1, md2, true, # links(m1, cache_dirs), m8, 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, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m1, cache_dirs) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ⟨let ino = inode.ino in if ino ∈ files then {files[ino].size := inode.size; files[ino].meta := inode.meta} else if ino ∈ dirs then dirs[ino].meta := inode.meta; p_inode := (m1 ∈ dirs ⊃ mkinode(m1, dirs[m1].meta, true, dirs[m1].nlink, dirs[m1].nsubdirs, dirs[m1].size) ;mkinode(m1, files[m1].meta, false, files[m1].nlink, 0, files[m1].size) ); c_inode := getinode(mkdentry(str, m5).ino, dirs, files); asynced := ?⟩ ( dirs = (cache_dirs[m1, mkdir(m6 + 1, md1, # links(m1, cache_dirs), m8 + 1, entries1[str, m5])] ++ m5)[m5, mkdir(0, md3, 1, 0, ∅)] [m1, mkdir(m, md2, m3, m4, entries0) ] ∧ files = (cache_files ⊕ cache_pcache) ⊕ cache_icache[m1, mkientry(false, mkinode(m1, md2, true, m3, m4, m))][m5, mkientry(false, mkinode(m5, md3, true, 1, 0, 0))] ∧ (asynced ↔ asynced0) ∧ mkinode(m1, md2, true, m3, m4, m) = p_inode ∧ mkinode(m5, md3, true, 1, 0, 0) = c_inode), m5 = 0, str ∈ entries1, m5 ∈ cache_files, m5 ∈ cache_dirs

Rule argument

pos: right 1

Additional information

Used simplifier rules: afs_inode_sync#(INODE; DIRS, FILES) {let INO = INODE.ino in if INO ∈ FILES then {FILES[INO].size := INODE.size; FILES[INO].meta := INODE.meta} else if INO ∈ DIRS then DIRS[INO].meta := INODE.meta };