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Proof step 122 from proof refine-readmeta (previous step)

files[m] = mkfile(m0, md1, # links(m, dirs), content), root.dir?, dom of < ino6, 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), pr(user, md1), px-parent(user, path, ROOT_INO, dirs, files), m ∈ files, ROOT_INO ∈ dirs, root[path].fid ∈ abs-files(files), psynced → asynced ⊦ root[path].dir?, m ∈ dirs, md1 = abs-files(files)[root[path].fid].meta ∧ # links(m, dirs) = count(root[path].fid, root.fids) ∧ m0 = # abs-files(files)[root[path].fid].content

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 123:
files[m] = mkfile(m0, md1, # links(m, dirs), content), root[path] = fnode(fid), root.dir?, dom of < ino6, 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), pr(user, md1), px-parent(user, path, ROOT_INO, dirs, files), fid ∈ abs-files(files), ROOT_INO ∈ dirs, m ∈ files, psynced → asynced ⊦ root[path].dir?, m ∈ dirs, md1 = abs-files(files)[fid].meta ∧ # links(m, dirs) = count(fid, root.fids) ∧ m0 = # abs-files(files)[fid].content

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