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Proof step 65 from proof refine-mkdir (previous step)

dirs[ino1] = mkdir(m, md0, m0, m1, entries), root[q].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), px-parent(user, q, ROOT_INO, dirs, files), ino1 ∈ dirs, psynced → asynced, ¬ px(user, md0) ∨ ¬ pw(user, md0) ⊦ ⟨posix_mkdir#(q + str ', md, user, abs-files(files), abs-of(of); err0, root; psynced)⟩ (abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ EACCESS = err0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 66:
⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n, md, n0, n1, entries) → # entries = n
Proof step 67:
dirs[ino1] = mkdir(# entries, md0, # links(ino1, dirs), m1, entries), root[q].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), px-parent(user, q, ROOT_INO, dirs, files), ino1 ∈ dirs, psynced → asynced, ¬ px(user, md0) ∨ ¬ pw(user, md0) ⊦ ⟨posix_mkdir#(q + str ', md, user, abs-files(files), abs-of(of); err0, root; psynced)⟩ (abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ EACCESS = err0)

Rule argument

Additional information

Used simplifier rules: make-abs-fold-work: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n, md, n0, n1, entries) → # entries = n;%afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n; (forward) from specification afs-base