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Proof step 20 from proof inv-unlink (previous step)

path ≠ ε, root0.dir?, fids-cons(root0, fs, ofh), py(user, parent(path), root0, fs), path ∈ root0, ¬ root0[path].dir? ⊦ ⟪psynced := ?⟫ fids-cons(root0 -- path, fs, ofh), ¬ root0[path].fid ∈ ofh.fids ∧ ¬ root0[path].fid ∈ root0.fids \ root0[path].fids

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 21:
root0[path] = fnode(fid), root0.dir?, fids-cons(root0, fs, ofh), py(user, parent(path), root0, fs), path ∈ root0 ⊦ ⟪psynced := ?⟫ fids-cons(root0 -- path, fs, ofh), path = ε, root0[path].dir?, ¬ fid ∈ ofh.fids ∧ ¬ fid ∈ root0.fids \ root0[path].fids

Rule argument

spec: directory-tree name: fnode-elim seq: ¬ tree.dir? ⊦ fid = tree.fid ↔ tree = fnode(fid) subst: [tree, fid] → [root0[path], fid0]

Additional information

Used simplifier rules: ¬ tree.dir? ⊦ fid = tree.fid ↔ tree = fnode(fid); (elim) Used terms: root0[path], fid0