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Proof step 23 from proof inv-create (previous step)

⟨afs_create_ino#(m, md, ino; dent, err, dirs, files)⟩ (dent = dent0 ∧ err = err0 ∧ dirs = dirs0 ∧ files = files0), dirs[m] = mkdir(m0, md2, # links(m, dirs), m2, entries0), dent = negdentry(str), ino ≠ 0, afs-cons(dirs0, files0), afs-cons(dirs, files), m ∈ dirs, ¬ ino ∈ dirs, ¬ ino ∈ files, ¬ str ∈ entries0, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [afs_inode_sync#(mkinode(m, md0, true, # links(m, dirs), m2, m0); dirs0, files0)] ( afs-cons(dirs0, files0) → ⟪p_inode := (m ∈ dirs0 ⊃ mkinode(m, dirs0[m].meta, true, dirs0[m].nlink, dirs0[m].nsubdirs, dirs0[m].size) ;mkinode(m, files0[m].meta, false, files0[m].nlink, 0, files0[m].size) ); c_inode := getinode(dent0.ino, dirs0, files0); asynced := ?⟫ true)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 24:
⟨afs_create_ino#(m, md, ino; dent, err, dirs1, files1)⟩ (dent = dent0 ∧ err = err0 ∧ dirs1 = dirs0 ∧ files1 = files0), dirs1[m] = mkdir(m0, md2, # links(m, dirs1), m2, entries0), dent = negdentry(str), dirs = dirs0, files = files0, inode = mkinode(m, md0, true, # links(m, dirs1), m2, m0), afs-cons(dirs1, files1), afs-cons(dirs0, files0), m ∈ dirs1, links(m, dirs1) ≠ ∅ ∨ 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(dent0.ino, dirs, files); asynced := ?⟫ true), ino = 0, ino ∈ dirs1, ino ∈ files1, str ∈ entries0

Rule argument

pos: right 1

Additional information

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