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

root.dir?, root[parent(path')].dir?, fids-cons(root, fs, ofh), px(user, parent(path), root, fs), py(user, parent(path'), root, fs), path ∈ root, parent(path') ∈ root, ¬ root[path].dir?, ¬ path' ∈ root ⊦ ⟪psynced := ?⟫ fids-cons(root[path', fnode(root[path].fid)], fs, ofh)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 11:
root[path] = fnode(fid), root[parent(path')].dir?, root.dir?, fids-cons(root, fs, ofh), px(user, parent(path), root, fs), py(user, parent(path'), root, fs), parent(path') ∈ root, path ∈ root ⊦ ⟪psynced := ?⟫ fids-cons(root[path', fnode(fid)], fs, ofh), root[path].dir?, path' ∈ root

Rule argument

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

Additional information

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