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Proof step 85 from proof refine-create (previous step)

# links(m1, cache_dirs) = m3, cache_dirs[m1] = mkdir(m2, md, # links(m1, cache_dirs), m5, entries0), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_dirs0 = cache_dirs, dent = negdentry(str), m ≠ 0, 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, ¬ str ∈ entries0, ¬ m ∈ cache_files, ¬ m ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m1, cache_dirs) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ∃ ino. ¬ ino ∈ cache_dirs ∧ ¬ ino ∈ afs_files ∧ ino ≠ 0 ∧ ⟨afs_create_ino#(m1, md0, ino; dent, err, cache_dirs, afs_files); afs_inode_sync#(mkinode(m1, md2, true, m3, m5, m2); cache_dirs, afs_files); p_inode := (m1 ∈ cache_dirs ⊃ mkinode(m1, cache_dirs[m1].meta, true, cache_dirs[m1].nlink, cache_dirs[m1].nsubdirs, cache_dirs[m1].size) ;mkinode(m1, afs_files[m1].meta, false, afs_files[m1].nlink, 0, afs_files[m1].size) ); c_inode := getinode(dent.ino, cache_dirs, afs_files); asynced := ?⟩ ( cache_dirs = cache_dirs0[m1, (m1 ∈ cache_dirs0 ⊃ mkdir(m2 + 1, md, # links(m1, cache_dirs0), m5, entries0[str, m]);cache_dirs0[m1]).meta:= md2] ∧ afs_files = ((cache_files ++ m)[m, mkfile(0, md0, 1, ∅)] ⊕ cache_pcache) ⊕ cache_icache[m1, mkientry(false, mkinode(m1, md2, true, # links(m1, cache_dirs0), m5, m2 + 1))] [m, mkientry (false, (m ∈ cache_dirs0 ⊃ mkinode (m, (m = m1 ⊃ mkdir(m2 + 1, md2, # links(m1, cache_dirs0), m5, entries0[str, m1]);cache_dirs0[m]).meta, true, (m = m1 ⊃ mkdir(m2 + 1, md2, # links(m1, cache_dirs0), m5, entries0[str, m1]);cache_dirs0[m]).nlink, (m = m1 ⊃ mkdir(m2 + 1, md2, # links(m1, cache_dirs0), m5, entries0[str, m1]);cache_dirs0[m]).nsubdirs, (m = m1 ⊃ mkdir(m2 + 1, md2, # links(m1, cache_dirs0), m5, entries0[str, m1]);cache_dirs0[m]).size) ;mkinode(m, md0, false, 1, 0, 0) )) ] ∧ (asynced ↔ asynced0) ∧ (m1 ∈ cache_dirs0 ⊃ mkinode(m1, md2, true, # links(m1, cache_dirs0), m5, m2 + 1) ;mkinode (m1, (m1 = m ⊃ mkfile(0, md0, 1, ∅);(cache_files ++ m)[m1]).meta, false, (m1 = m ⊃ mkfile(0, md0, 1, ∅);(cache_files ++ m)[m1]).nlink, 0, (m1 = m ⊃ mkfile(0, md0, 1, ∅);(cache_files ++ m)[m1]).size) ) = p_inode ∧ (m ∈ cache_dirs0 ⊃ mkinode (m, (m = m1 ⊃ mkdir(m2 + 1, md2, # links(m1, cache_dirs0), m5, entries0[str, m1]);cache_dirs0[m]).meta, true, (m = m1 ⊃ mkdir(m2 + 1, md2, # links(m1, cache_dirs0), m5, entries0[str, m1]);cache_dirs0[m]).nlink, (m = m1 ⊃ mkdir(m2 + 1, md2, # links(m1, cache_dirs0), m5, entries0[str, m1]);cache_dirs0[m]).nsubdirs, (m = m1 ⊃ mkdir(m2 + 1, md2, # links(m1, cache_dirs0), m5, entries0[str, m1]);cache_dirs0[m]).size) ;mkinode(m, md0, false, 1, 0, 0) ) = c_inode ∧ mkdentry(str, m) = dent ∧ ESUCCESS = err)

User applied rule exists right

And obtained the following new goals

Proof step 86:
# links(m1, cache_dirs) = m3, cache_dirs[m1] = mkdir(m2, md, # links(m1, cache_dirs), m5, entries0), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_dirs0 = cache_dirs, dent = negdentry(str), 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, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m1, cache_dirs) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ¬ m ∈ cache_dirs ∧ ¬ m ∈ afs_files ∧ m ≠ 0 ∧ ⟨afs_create_ino#(m1, md0, m; dent, err, cache_dirs, afs_files); afs_inode_sync#(mkinode(m1, md2, true, m3, m5, m2); cache_dirs, afs_files); p_inode := (m1 ∈ cache_dirs ⊃ mkinode(m1, cache_dirs[m1].meta, true, cache_dirs[m1].nlink, cache_dirs[m1].nsubdirs, cache_dirs[m1].size) ;mkinode(m1, afs_files[m1].meta, false, afs_files[m1].nlink, 0, afs_files[m1].size) ); c_inode := getinode(dent.ino, cache_dirs, afs_files); asynced := ?⟩ ( cache_dirs = cache_dirs0[m1, (m1 ∈ cache_dirs0 ⊃ mkdir(m2 + 1, md, # links(m1, cache_dirs0), m5, entries0[str, m]);cache_dirs0[m1]).meta:= md2] ∧ afs_files = ((cache_files ++ m)[m, mkfile(0, md0, 1, ∅)] ⊕ cache_pcache) ⊕ cache_icache[m1, mkientry(false, mkinode(m1, md2, true, # links(m1, cache_dirs0), m5, m2 + 1))] [m, mkientry (false, (m ∈ cache_dirs0 ⊃ mkinode (m, (m = m1 ⊃ mkdir(m2 + 1, md2, # links(m1, cache_dirs0), m5, entries0[str, m1]);cache_dirs0[m]).meta, true, (m = m1 ⊃ mkdir(m2 + 1, md2, # links(m1, cache_dirs0), m5, entries0[str, m1]);cache_dirs0[m]).nlink, (m = m1 ⊃ mkdir(m2 + 1, md2, # links(m1, cache_dirs0), m5, entries0[str, m1]);cache_dirs0[m]).nsubdirs, (m = m1 ⊃ mkdir(m2 + 1, md2, # links(m1, cache_dirs0), m5, entries0[str, m1]);cache_dirs0[m]).size) ;mkinode(m, md0, false, 1, 0, 0) )) ] ∧ (asynced ↔ asynced0) ∧ (m1 ∈ cache_dirs0 ⊃ mkinode(m1, md2, true, # links(m1, cache_dirs0), m5, m2 + 1) ;mkinode (m1, (m1 = m ⊃ mkfile(0, md0, 1, ∅);(cache_files ++ m)[m1]).meta, false, (m1 = m ⊃ mkfile(0, md0, 1, ∅);(cache_files ++ m)[m1]).nlink, 0, (m1 = m ⊃ mkfile(0, md0, 1, ∅);(cache_files ++ m)[m1]).size) ) = p_inode ∧ (m ∈ cache_dirs0 ⊃ mkinode (m, (m = m1 ⊃ mkdir(m2 + 1, md2, # links(m1, cache_dirs0), m5, entries0[str, m1]);cache_dirs0[m]).meta, true, (m = m1 ⊃ mkdir(m2 + 1, md2, # links(m1, cache_dirs0), m5, entries0[str, m1]);cache_dirs0[m]).nlink, (m = m1 ⊃ mkdir(m2 + 1, md2, # links(m1, cache_dirs0), m5, entries0[str, m1]);cache_dirs0[m]).nsubdirs, (m = m1 ⊃ mkdir(m2 + 1, md2, # links(m1, cache_dirs0), m5, entries0[str, m1]);cache_dirs0[m]).size) ;mkinode(m, md0, false, 1, 0, 0) ) = c_inode ∧ mkdentry(str, m) = dent ∧ ESUCCESS = err), m = 0, str ∈ entries0, m ∈ cache_files, m ∈ cache_dirs

Rule argument

pos: right 1 terms: m abort: F discard: T computed: T

Additional information

Used terms: m