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Proof step 12 from proof abs-nlinks-h (previous step)

tree[p] = fnode(⌜ino1⌝ ), links(ino1, dirs) = ∅, abs(tree, ino0)(dirs), ispath(p, ino0, dirs, files), ino1 ∈ files, ino0 ∈ dirs, p ∈ tree, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs, ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files ⊦ p = ε

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ p = ε ↔ ¬(∃ p0, str. p = p0 + str ')
Proof step 14:
tree[p] = fnode(⌜ino1⌝ ), links(ino1, dirs) = ∅, abs(tree, ino0)(dirs), ispath(p, ino0, dirs, files), p ∈ tree, ino0 ∈ dirs, ino1 ∈ files, ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs ⊦ ∀ p0, str. p ≠ p0 + str '

Rule argument

spec: list, inst: path name: lastdiv-rew seq: ⊦ p = ε ↔ ¬(∃ p0, str. p = p0 + str ') subst: [p] → [p] flags: <all paths>

Additional information

Used terms: p