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Proof step 27 from proof inv-mkdir (previous step)

# links(m, dirs0) = m1, dirs0[m] = mkdir(m0, md2, # links(m, dirs0), m2, entries0), 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, ∅) ], inode0 = mkinode(m, md0, true, m1, m2, m0), p_ino = m, afs-cons(dirs0, files), afs-cons(dirs, files), m ∈ dirs0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ [afs_inode_sync#(mkinode(m, md0, true, m1, m2, m0); dirs, files)] ( afs-cons(dirs, files) → ⟪p_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); c_inode := getinode(mkdentry(dent.name, ino).ino, dirs, files); asynced := ?⟫ afs-cons(dirs, files)), ino = 0, ino ∈ dirs0, ino ∈ files, str ∈ entries0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
dirs0[m] = mkdir(m0, md2, # links(m, dirs0), m2, entries0), dirs = (dirs0[m, mkdir(m0 + 1, md2, # links(m, dirs0), m2 + 1, entries0[str, ino])] ++ ino)[ino, mkdir(0, md, 1, 0, ∅)], ino ≠ 0, afs-cons(dirs0, files), afs-cons((dirs0[m, mkdir(m0 + 1, md2, # links(m, dirs0), m2 + 1, entries0[str, ino])] ++ ino)[ino, mkdir(0, md, 1, 0, ∅)], files), m ∈ dirs0, ¬ ino ∈ dirs0, ¬ ino ∈ files, ¬ str ∈ entries0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ [afs_inode_sync#(mkinode(m, md0, true, # links(m, dirs0), m2, m0); dirs, files)] ( afs-cons(dirs, files) → ⟪p_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); c_inode := getinode(mkdentry(str, ino).ino, dirs, files); asynced := ?⟫ true)

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries).nsubdirs:= m4 = mkdir(m, md, m0, m4, entries); (s)% ⊦ mkdir(m, md, m0, m1, entries).nsubdirs = m1; (s)%⊦ 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)% ⊦ (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)