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Proof step 76 from proof refine-readmeta (previous step)

root[path] = dnode(md1, sdt), ((m => mkdir(# entries0, md1, # links(m, dirs), # subdirs(m, dirs), entries0) * abs(sdt, entries0) * abs|(root, ROOT_INO, path, m)) )(dirs), root.dir?, dom of < ino6, 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), path ∈ root, ROOT_INO ∈ dirs, # links(m, dirs) ≤ 1, psynced → asynced, m ≠ ROOT_INO ∧ links(m, dirs) = ∅ → entries0 = ∅, ∀ name. name ∈ entries0 → entries0[name] ∈ dirs ∨ entries0[name] ∈ files, ∀ ino. (ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dirs[ino].entries = ∅) ∧ ( ino ∈ dirs → ¬ ino ∈ files ∧ dirs[ino].nlink = # links(ino, dirs) ∧ dirs[ino].nlink ≤ 1 ∧ dirs[ino].size = # dirs[ino].entries ∧ dirs[ino].nsubdirs = # subdirs(ino, dirs)) ∧ (ino ∈ files → ¬ ino ∈ dirs ∧ files[ino].nlink = # links(ino, dirs)) ∧ (∀ name. ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files) ∧ (∀ n. ino ∈ files ∧ n ∈ files[ino].content → # files[ino].content[n] = VFS_PAGE_SIZE) ⊦ # subdirs(m, dirs) = # dnode(md1, sdt).subdirs, str ∈ dirs[m].entries ∧ dirs[m].entries[str] ∈ dirs ↔ str ∈ sdt ∧ sdt[str].dir?, m ∈ files

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 77:
root[path] = dnode(md1, sdt), dirs[m] = mkdir(m0, md, m1, m2, entries), ((m => mkdir(# entries0, md1, # links(m, dirs), # subdirs(m, dirs), entries0) * abs(sdt, entries0) * abs|(root, ROOT_INO, path, m)) )(dirs), root.dir?, dom of < ino6, 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), ROOT_INO ∈ dirs, path ∈ root, # links(m, dirs) ≤ 1, m ≠ ROOT_INO ∧ links(m, dirs) = ∅ → entries0 = ∅, psynced → asynced, ∀ ino. (ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dirs[ino].entries = ∅) ∧ ( ino ∈ dirs → ¬ ino ∈ files ∧ dirs[ino].nlink = # links(ino, dirs) ∧ dirs[ino].nlink ≤ 1 ∧ dirs[ino].size = # dirs[ino].entries ∧ dirs[ino].nsubdirs = # subdirs(ino, dirs)) ∧ (ino ∈ files → ¬ ino ∈ dirs ∧ files[ino].nlink = # links(ino, dirs)) ∧ (∀ name. ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files) ∧ (∀ n. ino ∈ files ∧ n ∈ files[ino].content → # files[ino].content[n] = VFS_PAGE_SIZE), ∀ name. name ∈ entries0 → entries0[name] ∈ dirs ∨ entries0[name] ∈ files ⊦ # subdirs(m, dirs) = # dnode(md1, sdt).subdirs, str ∈ entries ∧ entries[str] ∈ dirs ↔ str ∈ sdt ∧ sdt[str].dir?, m ∈ files

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [dirs[m], m0, md, m1, m2, entries]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: dirs[m], m0, md, m1, m2, entries