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Proof step 105 from proof refine-writemeta (previous step)

files[m] = mkfile(m0, md0, # links(m, dirs), content), root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, m, dirs, files), of-cons(of, dirs, files), pw(user, md0), px-parent(user, path, ROOT_INO, dirs, files), m ∈ files, ROOT_INO ∈ dirs, root[path].fid ∈ abs-files(files), ¬ root[path].dir?, ¬ m ∈ dirs, psynced → asynced0 ⊦ ⟨psynced := ?⟩ ( abs-files(files)[root[path].fid, mkfile(md, abs-files(files)[root[path].fid].content)] = abs-files(files[m, mkfile(m0, md, # links(m, dirs), content)]) ∧ (psynced → asynced))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 106:
files[m] = mkfile(m0, md0, # links(m, dirs), content), root[path] = fnode(fid), root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, m, dirs, files), of-cons(of, dirs, files), pw(user, md0), px-parent(user, path, ROOT_INO, dirs, files), fid ∈ abs-files(files), ROOT_INO ∈ dirs, m ∈ files, psynced → asynced0 ⊦ ⟨psynced := ?⟩ ( abs-files(files)[fid, mkfile(md, abs-files(files)[fid].content)] = abs-files(files[m, mkfile(m0, md, # links(m, dirs), content)]) ∧ (psynced → asynced)), root[path].dir?, m ∈ dirs

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