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Proof step 9 from proof inv-writemeta (previous step)

root[path].dir?, root.dir?, fids-cons(root, fs, ofh), pw(user, path, root, fs), path ∈ root ⊦ ⟪psynced := ?⟫ fids-cons(root[path, dnode(md, root[path].entries)], fs, ofh)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 10:
root[path] = dnode(md0, sdt), root.dir?, root[path].dir?, fids-cons(root, fs, ofh), pw(user, path, root, fs), path ∈ root ⊦ ⟪psynced := ?⟫ fids-cons(root[path, dnode(md, sdt)], fs, ofh)

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], md0, sdt]

Additional information

Used simplifier rules: tree.dir? ⊦ md = tree.meta ∧ sdt = tree.entries ↔ tree = dnode(md, sdt); (elim) Used terms: root[path], md0, sdt