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Proof step 3 from proof afs-cons-mkdir-ino (previous step)

p_inode.nlink = dirs[p_inode.ino].nlink, p_inode.nsubdirs = dirs[p_inode.ino].nsubdirs, p_inode.size = dirs[p_inode.ino].size, ino ≠ 0, p_inode.directory, dent.negdentry?, afs-cons(dirs, files), p_inode.ino ∈ dirs, ¬ ino ∈ files, ¬ ino ∈ dirs, ¬ dent.name ∈ dirs[p_inode.ino].entries, links(p_inode.ino, dirs) ≠ ∅ ∨ p_inode.ino = ROOT_INO ⊦ ⟪afs_mkdir_ino#(p_inode.ino, md, ino; dent, err, dirs)⟫ afs-cons(dirs, files)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
p_inode.nlink = dirs[p_inode.ino].nlink, p_inode.nsubdirs = dirs[p_inode.ino].nsubdirs, p_inode.size = dirs[p_inode.ino].size, dent = negdentry(str), p_inode.directory, dent.negdentry?, afs-cons(dirs, files), p_inode.ino ∈ dirs, links(p_inode.ino, dirs) ≠ ∅ ∨ p_inode.ino = ROOT_INO ⊦ ⟪afs_mkdir_ino#(p_inode.ino, md, ino; dent, err, dirs)⟫ afs-cons(dirs, files), ino = 0, ino ∈ files, ino ∈ dirs, str ∈ dirs[p_inode.ino].entries

Rule argument

spec: dentry name: elim-02 seq: ⊦ dent.negdentry? → (str = dent.name ↔ dent = negdentry(str)) subst: [dent, str] → [dent, str]

Additional information

Used simplifier rules: ⊦ dent.negdentry? → (str = dent.name ↔ dent = negdentry(str)); (elim) Used terms: dent, str