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Proof step 78 from proof refine-open (previous step)

files[ino0] = mkfile(m, md, # links(ino0, dirs), content), 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), of-cons(of[ino2, mkfile(ino0, mode, 0)], dirs, files), px-parent(user, path, ROOT_INO, dirs, files), ino0 ∈ files, ROOT_INO ∈ dirs, psynced → asynced ⊦ pre-open(path, mode, ESUCCESS, user, root, abs-files(files), ofh) ∧ ⟨err0 := ESUCCESS; 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[fd, mkfile(ino0, mode, 0)]) ∧ (psynced → asynced) ∧ ino2 = fd ∧ ESUCCESS = err0), ∃ err. pre-open(path, mode, err, user, root, abs-files(files), ofh) ∧ ⟨err0 := err; 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[fd, mkfile(ino0, mode, 0)]) ∧ (psynced → asynced) ∧ ino2 = fd ∧ ESUCCESS = err0), root[path].dir?, ino0 ∈ dirs, (mode = MODE_W ∨ mode = MODE_RW) ∧ ¬ pw(user, md), (mode = MODE_R ∨ mode = MODE_RW) ∧ ¬ pr(user, md)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 79:
⊦ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (p ∈ tree ↔ ispath(p, ino, dirs, files))
Proof step 80:
⊦ 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 81:
⊦ 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 82:
files[ino0] = mkfile(m, md, # links(ino0, dirs), content), 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), of-cons(of[ino2, mkfile(ino0, mode, 0)], dirs, files), px-parent(user, path, ROOT_INO, dirs, files), ino0 ∈ files, ROOT_INO ∈ dirs, ¬ root[path].dir?, ¬ ino0 ∈ dirs, psynced → asynced ⊦ ∃ err. pre-open(path, mode, err, user, root, abs-files(files), ofh) ∧ ⟨err0 := err; 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[fd, mkfile(ino0, mode, 0)]) ∧ (psynced → asynced) ∧ ino2 = fd ∧ ESUCCESS = err0), (mode = MODE_R ∨ mode = MODE_RW → pr(user, md)) ∧ (mode = MODE_W ∨ mode = MODE_RW → pw(user, md)) ∧ ⟨err0 := ESUCCESS; 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[fd, mkfile(ino0, mode, 0)]) ∧ (psynced → asynced) ∧ ino2 = fd ∧ ESUCCESS = err0), (mode = MODE_W ∨ mode = MODE_RW) ∧ ¬ pw(user, md), (mode = MODE_R ∨ mode = MODE_RW) ∧ ¬ pr(user, md)

Rule argument

Additional information

Used simplifier rules: path-in-eq: ⊦ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (p ∈ tree ↔ ispath(p, ino, dirs, files));%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)% ⊦ ispath(p, n, m, dirs, files) → ispath(p, n, dirs, files); (s)%⊦ pre-open(p, mode, ESUCCESS, user, root, fs, ofh) ↔ p ∈ root ∧ ¬ root[p].dir? ∧ (mode = MODE_R ∨ mode = MODE_RW → pr(user, p, root, fs)) ∧ (mode = MODE_W ∨ mode = MODE_RW → pw(user, p, root, fs)); (s)