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Proof step 10 from proof inv-rmdir (previous step)

root[path].entries = ∅, fid ∈ fs ↔ fid ∈ root.fids ∨ fid ∈ ofh.fids, root.dir?, root[path].dir?, fids-cons(root, fs, ofh), py(user, parent(path), root, fs), path ∈ root ⊦ fid ∈ fs ↔ fid ∈ root.fids \ root[path].fids ∨ fid ∈ ofh.fids, path = ε

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: directory-tree name: dnode-elim seq: tree.dir? ⊦ md = tree.meta ∧ sdt = tree.entries ↔ tree = dnode(md, sdt) subst: [tree, md, sdt] → [root[path], md, sdt]

Additional information

Used simplifier rules: ⊦ dnode(md, sdt).fids = sdt.fids; (s)% ⊦ ∅.fids = ∅; (s)% ⊦ fidb \ ∅ = fidb; (s)%tree.dir? ⊦ md = tree.meta ∧ sdt = tree.entries ↔ tree = dnode(md, sdt); (elim) Used terms: root[path], md, sdt