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Proof step 52 from proof refine-readdir (previous step)

dirs[ino1] = mkdir(m, md, m0, m1, entries), strings = strings0, root[path].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(path, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), px-parent(user, path, ROOT_INO, dirs, files), ino1 ∈ dirs, psynced → asynced ⊦ ⟨posix_readdir#(path, user, root, abs-files(files), abs-of(of); strings0, err0)⟩ ((psynced → asynced) ∧ strings = strings0 ∧ EACCESS = err0), pr(user, md)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 53:
⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n, md, n0, n1, entries) → # entries = n
Proof step 54:
dirs[ino1] = mkdir(# entries, md, # links(ino1, dirs), m1, entries), strings = strings0, root[path].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(path, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), px-parent(user, path, ROOT_INO, dirs, files), ino1 ∈ dirs, ¬ pr(user, md), psynced → asynced ⊦ ⟨posix_readdir#(path, user, root, abs-files(files), abs-of(of); strings0, err0)⟩ ((psynced → asynced) ∧ strings = strings0 ∧ 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