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Proof step 56 from proof refine-open (previous step)

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, psynced → asynced, (mode = MODE_R ∨ mode = MODE_RW) ∧ ¬ pr(user, md) ∨ (mode = MODE_W ∨ mode = MODE_RW) ∧ ¬ pw(user, md) ⊦ pre-open(path, mode, EACCESS, user, root, abs-files(files), ofh) ∧ ⟨err0 := EACCESS; if err0 = ESUCCESS then let fid = root[path].fid in choose n with ¬ n ∈ ofh in {ofh[n] := mkfh(fid, mode, 0); fd := n}⟩ (ofh = abs-of(of) ∧ (psynced → asynced) ∧ ino1 = fd ∧ EACCESS = err0), root[path].dir?, ino0 ∈ dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 57:
⊦ 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 58:
⊦ 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) → (pw(user, p, tree, abs-files(files)) ↔ pw(user, meta(ε, m, dirs, files)))
Proof step 59:
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) ⊦ ( (mode = MODE_R ∨ mode = MODE_RW) ∧ ¬ pr(user, md) ∨ (mode = MODE_W ∨ mode = MODE_RW) ∧ ¬ pw(user, md) ∨ ¬ px(user, parent(path), root, abs-files(files))) ∧ ⟨err0 := EACCESS; if err0 = ESUCCESS then let fid = root[path].fid in choose n with ¬ n ∈ ofh in {ofh[n] := mkfh(fid, mode, 0); fd := n}⟩ (ofh = abs-of(of) ∧ (psynced → asynced) ∧ ino1 = fd ∧ 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)));%pw: ⊦ 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) → ( pw(user, p, tree, abs-files(files)) ↔ pw(user, meta(ε, m, dirs, files)));% ⊦ mkfile(m, md, m0, content).meta = md; (s)%¬ ino ∈ dirs ⊦ ino ∈ files → meta(ε, ino, dirs, files) = files[ino].meta; (s)%⊦ pre-open(p, mode, EACCESS, user, root, fs, ofh) ↔ (mode = MODE_R ∨ mode = MODE_RW) ∧ ¬ pr(user, p, root, fs) ∨ (mode = MODE_W ∨ mode = MODE_RW) ∧ ¬ pw(user, p, root, fs) ∨ ¬ px(user, parent(p), root, fs); (s)