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Proof step 28 from proof inv-mkdir (previous step)

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)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 29:
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, ∅)], inode = mkinode(m, md0, true, # links(m, dirs0), m2, m0), afs-cons((dirs0[m, mkdir(m0 + 1, md2, # links(m, dirs0), m2 + 1, entries0[str, ino])] ++ ino)[ino, mkdir(0, md, 1, 0, ∅)], files), afs-cons(dirs0, files), m ∈ dirs0, links(m, dirs0) ≠ ∅ ∨ m = 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] ( 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), ino = 0, ino ∈ dirs0, ino ∈ files, str ∈ entries0

Rule argument

pos: right 1

Additional information

Used simplifier rules: internal-inode-sync: ⊦ ;