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Proof step 58 from proof refine-readdir (previous step)

dirs[ino1] = mkdir(# entries, md, # links(ino1, dirs), m1, entries), 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 ⊦ pre-readdir(path, EACCESS, user, root, abs-files(files), abs-of(of)) ∧ ⟨err0 := EACCESS; if err0 = ESUCCESS then strings := dom root[path].entries else strings := ?⟩ ((psynced → asynced) ∧ strings0 = strings ∧ EACCESS = err0), pr(user, md)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 59:
⊦ ispath(p, ino, m, dirs, files) ∧ px-parent(user, p, ino, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (pr(user, p, tree, abs-files(files)) ↔ pr(user, meta(ε, m, dirs, files)))
Proof step 60:
dirs[ino1] = mkdir(# entries, md, # links(ino1, dirs), m1, entries), 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 ⊦ ⟨err0 := EACCESS; if err0 = ESUCCESS then strings := dom root[path].entries else strings := ?⟩ ((psynced → asynced) ∧ strings0 = strings ∧ EACCESS = err0)

Rule argument

Additional information

Used simplifier rules: pr: ⊦ ispath(p, ino, m, dirs, files) ∧ px-parent(user, p, ino, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → ( pr(user, p, tree, abs-files(files)) ↔ pr(user, meta(ε, m, dirs, files)));% ⊦ mkdir(m, md, m0, m1, entries).meta = md; (s)% ⊦ ino ∈ dirs → meta(ε, ino, dirs, files) = dirs[ino].meta; (s)%⊦ pre-readdir(p, EACCESS, user, root, fs, ofh) ↔ ¬ pr(user, p, root, fs); (s)