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Proof step 4 from proof abs-nlinks-h (previous step)

links(ino1, dirs) = ∅, abs(tree, ino0)(dirs), ⌜ino1⌝ ∈ tree.fids, ino0 ∈ dirs, ino1 ∈ files, ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ fid ∈ tree.fids ↔ (∃ p. p ∈ tree ∧ tree[p] = fnode(fid))
Proof step 6:
links(ino1, dirs) = ∅, abs(tree, ino0)(dirs), ino1 ∈ files, ino0 ∈ dirs, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs, ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files, ∃ p. p ∈ tree ∧ tree[p] = fnode(⌜ino1⌝ ) ⊦

Rule argument

spec: directory-tree-fids name: fids-in seq: ⊦ fid ∈ tree.fids ↔ (∃ p. p ∈ tree ∧ tree[p] = fnode(fid)) subst: [tree, fid] → [tree, ⌜ino1⌝ ] flags: <all paths>

Additional information

Used terms: tree, ⌜ino1⌝