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Proof step 80 from proof refine-readmeta (previous step)

root[path] = dnode(md1, sdt), 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, str ∈ sdt, # links(m, dirs) ≤ 1, psynced → asynced, m ≠ ROOT_INO ∧ links(m, dirs) = ∅ → entries = ∅, ∀ name. name ∈ entries → entries[name] ∈ dirs ∨ entries[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), ∃ tree, ino, sdi0, sdt0. ¬ str ∈ sdt0 ∧ sdt = sdt0[str, tree] ∧ ¬ str ∈ sdi0 ∧ entries = sdi0[str, ino] ∧ (( abs(tree, ino) * abs(sdt0, sdi0) * abs|(root, ROOT_INO, path, m) * m => mkdir(# entries, md1, # links(m, dirs), # subdirs(m, dirs), entries)) )(dirs) ⊦ # subdirs(m, dirs) = # dnode(md1, sdt).subdirs, str ∈ entries ∧ entries[str] ∈ dirs ↔ str ∈ sdt ∧ sdt[str].dir?, m ∈ files

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 81:
root[path] = dnode(md1, sdt0[str, tree]), (( abs(tree, ino) * abs(sdt0, sdi) * abs|(root, ROOT_INO, path, m) * m => mkdir(# sdi + 1, md1, # links(m, dirs), # subdirs(m, dirs), sdi[str, ino])) )(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, 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 ∈ sdi[str, ino] → sdi[str, ino][name] ∈ dirs ∨ sdi[str, ino][name] ∈ files ⊦ # subdirs(m, dirs) = # dnode(md1, sdt0[str, tree]).subdirs, ino ∈ dirs ↔ tree.dir?, m ∈ files, str ∈ sdi, str ∈ sdt0, m ≠ ROOT_INO ∧ links(m, dirs) = ∅

Rule argument

Additional information

Used simplifier rules: ⊦ entries[str, ino] ≠ ∅; (s)% ⊦ str ∈ sdt[str0, tree] ↔ str = str0 ∨ str ∈ sdt; (ws)% ⊦ ¬ str ∈ entries → # entries[str, ino] = # entries + 1; (s)% ⊦ sdt[str, tree][str] = tree; (s)% ⊦ str ∈ sdt[str, tree]; (s)% ⊦ entries[str, ino][str] = ino; (s)% ⊦ str ∈ entries[str, ino]; (s)