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Proof step 95 from proof refine-create (previous step)

# links(m1, cache_dirs) = m3, cache_dirs[m1] = mkdir(m2, md1, # links(m1, cache_dirs), m5, entries0), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_dirs0 = cache_dirs, dent = negdentry(str), dirs = dirs0[p_ino, dirs0[p_ino].entries:= dirs0[p_ino].entries[dent.name, ino]] [p_ino, dirs0[p_ino, dirs0[p_ino].entries:= dirs0[p_ino].entries[dent.name, ino]][p_ino] .size:= (dirs0[p_ino, dirs0[p_ino].entries:= dirs0[p_ino].entries[dent.name, ino]][p_ino].size + 1) ], dirs0 = cache_dirs, files = (files0 ++ ino)[ino, mkfile(0, md, 1, ∅)], files0 = afs_files, ino = m, md = md0, p_ino = m1, 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 ⊦ ⟨afs_inode_sync#(mkinode(m1, md2, true, m3, m5, m2); dirs, files); 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(dent.name, ino).ino, dirs, files); asynced := ?⟩ ( dirs = cache_dirs0[m1, (m1 ∈ cache_dirs0 ⊃ mkdir(m2 + 1, md1, # links(m1, cache_dirs0), m5, entries0[str, m]);cache_dirs0[m1]).meta:= md2] ∧ 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) = mkdentry(dent.name, ino) ∧ ESUCCESS = ESUCCESS), m = 0, str ∈ entries0, m ∈ cache_files, m ∈ cache_dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 96:
cache_dirs[m1] = mkdir(m2, md1, # links(m1, cache_dirs), m5, entries0), dirs = cache_dirs[m1, mkdir(m2 + 1, md1, # links(m1, cache_dirs), m5, entries0[str, m])], files = (((cache_files ⊕ cache_pcache) ⊕ cache_icache) ++ m)[m, mkfile(0, md0, 1, ∅)], 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 ⊦ ⟨afs_inode_sync#(mkinode(m1, md2, true, # links(m1, cache_dirs), m5, m2); dirs, files); 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, m).ino, dirs, files); asynced := ?⟩ ( dirs = cache_dirs[m1, mkdir(m2 + 1, md2, # links(m1, cache_dirs), m5, entries0[str, m])] ∧ files = ((cache_files ++ m)[m, mkfile(0, md0, 1, ∅)] ⊕ cache_pcache) ⊕ 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)) ] ∧ (asynced ↔ asynced0) ∧ mkinode(m1, md2, true, # links(m1, cache_dirs), m5, m2 + 1) = p_inode ∧ mkinode(m, md0, false, 1, 0, 0) = c_inode)

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries).size:= m2 = mkdir(m2, md, m0, m1, entries); (s)% ⊦ mkdir(m, md, m0, m1, entries).size = m; (s)%⊦ mkdir(m, md, m0, m1, entries).entries:= entries0 = mkdir(m, md, m0, m1, entries0); (s)% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)%⊦ mkdir(m, md, m0, m1, entries).meta:= md0 = mkdir(m, md0, m0, m1, entries); (s)% ⊦ dirs[ino, ad][ino, ad0] = dirs[ino, ad0]; (s)% ⊦ (ad.entries:= entries).size = ad.size; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ negdentry(str).name = str; (s)