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Proof step 230 from proof refine-truncate (previous step)

files0[ino2] = mkfile(m0, md0, # links(ino2, dirs), content0), root.dir?, dom of < ino3, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files0[ino2, mkfile(n, md0, # links(ino2, dirs), content0 upto min(n, m0))]), afs-cons(dirs, files0), fids-cons(root, abs-files(files0), abs-of(of)), ispath(path, ROOT_INO, ino2, dirs, files0), of-cons(of, dirs, files0[ino2, mkfile(n, md0, # links(ino2, dirs), content0 upto min(n, m0))]), of-cons(of, dirs, files0), pw(user, md0), px-parent(user, path, ROOT_INO, dirs, files0), root[path].fid ∈ abs-files(files0), ROOT_INO ∈ dirs, ino2 ∈ files0, ¬ root[path].dir?, ¬ ino2 ∈ dirs, psynced → asynced0 ⊦ ⟨psynced := ?⟩ ( abs-files(files0)[root[path].fid, mkfile(abs-files(files0)[root[path].fid].meta, resize(abs-files(files0)[root[path].fid].content, n))] = abs-files(files0[ino2, mkfile(n, md0, # links(ino2, dirs), content0 upto min(n, m0))]) ∧ (psynced → asynced)), m0 ≤ n ∧ m0 % VFS_PAGE_SIZE ≠ 0 ∧ m0 / VFS_PAGE_SIZE ∈ content0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 231:
files0[ino2] = mkfile(m0, md0, # links(ino2, dirs), content0), root[path] = fnode(fid), root.dir?, dom of < ino3, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files0), afs-cons(dirs, files0[ino2, mkfile(n, md0, # links(ino2, dirs), content0 upto min(n, m0))]), fids-cons(root, abs-files(files0), abs-of(of)), ispath(path, ROOT_INO, ino2, dirs, files0), of-cons(of, dirs, files0), of-cons(of, dirs, files0[ino2, mkfile(n, md0, # links(ino2, dirs), content0 upto min(n, m0))]), pw(user, md0), px-parent(user, path, ROOT_INO, dirs, files0), ino2 ∈ files0, ROOT_INO ∈ dirs, fid ∈ abs-files(files0), psynced → asynced0 ⊦ ⟨psynced := ?⟩ ( abs-files(files0)[fid, mkfile(abs-files(files0)[fid].meta, resize(abs-files(files0)[fid].content, n))] = abs-files(files0[ino2, mkfile(n, md0, # links(ino2, dirs), content0 upto min(n, m0))]) ∧ (psynced → asynced)), root[path].dir?, ino2 ∈ dirs, m0 ≤ n ∧ m0 % VFS_PAGE_SIZE ≠ 0 ∧ m0 / VFS_PAGE_SIZE ∈ content0

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