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Proof step 51 from proof refine-open (previous step)

files[ino0] = mkfile(m, md, m0, content), fd = ino1, ofh = abs-of(of), root.dir?, dom of < ino2, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), px-parent(user, path, ROOT_INO, dirs, files), ino0 ∈ files, ROOT_INO ∈ dirs, psynced → asynced, (mode = MODE_R ∨ mode = MODE_RW) ∧ ¬ pr(user, md) ∨ (mode = MODE_W ∨ mode = MODE_RW) ∧ ¬ pw(user, md) ⊦ ⟨posix_open#(path, mode, user, root, abs-files(files); ino1, err0, ofh)⟩ (ofh = abs-of(of) ∧ (psynced → asynced) ∧ fd = ino1 ∧ EACCESS = err0), root[path].dir?, ino0 ∈ dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 52:
files[ino0] = mkfile(m, md, # links(ino0, dirs), content), fd = ino1, ofh = abs-of(of), root.dir?, dom of < ino2, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), px-parent(user, path, ROOT_INO, dirs, files), ino0 ∈ files, ROOT_INO ∈ dirs, ¬ root[path].dir?, ¬ ino0 ∈ dirs, psynced → asynced, (mode = MODE_R ∨ mode = MODE_RW) ∧ ¬ pr(user, md) ∨ (mode = MODE_W ∨ mode = MODE_RW) ∧ ¬ pw(user, md) ⊦ ⟨posix_open#(path, mode, user, root, abs-files(files); ino1, err0, ofh)⟩ (ofh = abs-of(of) ∧ (psynced → asynced) ∧ fd = ino1 ∧ EACCESS = err0)

Rule argument

Additional information

Used simplifier rules: afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base