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Proof step 99 from proof refine-mkdir (previous step)

# links(m1, cache_dirs) = m7, (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, 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) ] [p_ino, 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) ] [p_ino ] .nsubdirs:= ( 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) ] [p_ino ] .nsubdirs + 1) ] ++ ino )[ino, mkdir(0, md, 1, 0, ∅) ], dirs0 = cache_dirs, ino = m5, md = md3, p_ino = m1, 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 ⊦ ⟨afs_inode_sync#(mkinode(m1, md2, true, m7, 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(dent.name, ino).ino, dirs, afs_files); asynced := ?⟩ ( dirs = (cache_dirs0[m1, mkdir(m6 + 1, md1, # links(m1, cache_dirs0), m8 + 1, entries1[str, m5])] ++ m5)[m5, mkdir(0, md3, 1, 0, ∅)] [m1, (m1 = m5 ∧ m5 ∈ cache_dirs0[m5, mkdir(m6 + 1, md1, # links(m5, cache_dirs0), m8 + 1, entries1[str, m5])] ++ m5 ⊃ mkdir(0, md3, 1, 0, ∅) ;(cache_dirs0[m1, mkdir(m6 + 1, md1, # links(m1, cache_dirs0), m8 + 1, entries1[str, m5])] ++ m5)[m1] ) .meta:= md2 ] ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache[m1, mkientry(false, mkinode(m1, md2, true, m3, m4, m))] [m5, mkientry (false, (m5 ∈ cache_dirs0[m1, mkdir(m6 + 1, md1, # links(m1, cache_dirs0), m8 + 1, entries1[str, m5])] ++ m5 ⊃ mkinode (m5, (m5 = m1 ⊃ mkdir(m, md2, m3, m4, entries0);mkdir(0, md3, 1, 0, ∅)).meta, true, (m5 = m1 ⊃ mkdir(m, md2, m3, m4, entries0);mkdir(0, md3, 1, 0, ∅)).nlink, (m5 = m1 ⊃ mkdir(m, md2, m3, m4, entries0);mkdir(0, md3, 1, 0, ∅)).nsubdirs, (m5 = m1 ⊃ mkdir(m, md2, m3, m4, entries0);mkdir(0, md3, 1, 0, ∅)).size) ;mkinode(m5, cache_files[m5].meta, false, cache_files[m5].nlink, 0, cache_files[m5].size) )) ] ∧ (asynced ↔ asynced0) ∧ (m1 ∈ cache_dirs0[m1, mkdir(m6 + 1, md1, # links(m1, cache_dirs0), m8 + 1, entries1[str, m5])] ++ m5 ⊃ mkinode (m1, md2, true, (m1 = m5 ⊃ mkdir(0, md3, 1, 0, ∅) ;(cache_dirs0[m1, mkdir(m6 + 1, md1, # links(m1, cache_dirs0), m8 + 1, entries1[str, m5])] ++ m5)[m1] ) .nlink, (m1 = m5 ⊃ mkdir(0, md3, 1, 0, ∅) ;(cache_dirs0[m1, mkdir(m6 + 1, md1, # links(m1, cache_dirs0), m8 + 1, entries1[str, m5])] ++ m5)[m1] ) .nsubdirs, (m1 = m5 ⊃ mkdir(0, md3, 1, 0, ∅) ;(cache_dirs0[m1, mkdir(m6 + 1, md1, # links(m1, cache_dirs0), m8 + 1, entries1[str, m5])] ++ m5)[m1] ) .size) ;mkinode(m1, cache_files[m1].meta, false, cache_files[m1].nlink, 0, cache_files[m1].size) ) = p_inode ∧ (m5 ∈ cache_dirs0[m1, mkdir(m6 + 1, md1, # links(m1, cache_dirs0), m8 + 1, entries1[str, m5])] ++ m5 ⊃ mkinode (m5, (m5 = m1 ⊃ mkdir(0, md2, 1, 0, ∅);mkdir(0, md3, 1, 0, ∅)).meta, true, (m5 = m1 ⊃ mkdir(0, md2, 1, 0, ∅);mkdir(0, md3, 1, 0, ∅)).nlink, (m5 = m1 ⊃ mkdir(0, md2, 1, 0, ∅);mkdir(0, md3, 1, 0, ∅)).nsubdirs, (m5 = m1 ⊃ mkdir(0, md2, 1, 0, ∅);mkdir(0, md3, 1, 0, ∅)).size) ;mkinode(m5, cache_files[m5].meta, false, cache_files[m5].nlink, 0, cache_files[m5].size) ) = c_inode ∧ mkdentry(str, m5) = mkdentry(dent.name, ino) ∧ ESUCCESS = ESUCCESS), m5 = 0, str ∈ entries1, m5 ∈ cache_files, m5 ∈ cache_dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries).meta:= md0 = mkdir(m, md0, m0, m1, entries); (s)%⊦ mkdir(m, md, m0, m1, entries).nsubdirs:= m4 = mkdir(m, md, m0, m4, entries); (s)%⊦ mkdir(m, md, m0, m1, entries).size:= m2 = mkdir(m2, md, m0, m1, entries); (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).size = m; (s)% ⊦ mkdir(m, md, m0, m1, entries).nsubdirs = m1; (s)% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)% ⊦ mkdir(m, md, m0, m1, entries).meta = md; (s)%ino ≠ 0, ¬ ino ∈ dirs ⊦ ino0 ∈ dirs ++ ino ↔ ino0 = ino ∨ ino0 ∈ dirs; (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)% ⊦ (ad.entries:= entries).nsubdirs = ad.nsubdirs; (s)% ⊦ (ad.size:= m).nsubdirs = ad.nsubdirs; (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)