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Proof step 11 from proof inv-truncate (previous step)

root.dir?, fids-cons(root, fs, ofh), pw(user, path, root, fs), root[path].fid ∈ fs, path ∈ root, ¬ root[path].dir? ⊦ ⟪psynced := ?⟫ fids-cons(root, fs[root[path].fid, mkfile(fs[root[path].fid].meta, resize(fs[root[path].fid].content, n))], ofh)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
root[path] = fnode(fid), root.dir?, fids-cons(root, fs, ofh), pw(user, path, root, fs), path ∈ root, fid ∈ fs ⊦ ⟪psynced := ?⟫ fids-cons(root, fs[fid, mkfile(fs[fid].meta, resize(fs[fid].content, n))], ofh), root[path].dir?

Rule argument

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

Additional information

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