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Proof step 76 from proof refine-create (previous step)

dirs[ino1] = mkdir(# entries, md0, # links(ino1, dirs), m1, entries), fs = abs-files(files), path = q + str ', root[q].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(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), px-parent(user, q, ROOT_INO, dirs, files), ino1 ∈ dirs, psynced → asynced, ¬ px(user, md0) ∨ ¬ pw(user, md0) ⊦ ¬ py(user, parent(path), root, fs) ∧ ⟨err0 := EACCESS; if err0 = ESUCCESS then choose fid with ¬ fid ∈ fs in {root[path] := fnode(fid); fs[fid] := mkfile(md, mkbuf(0))}; psynced := ?⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ EACCESS = err0)

Heuristic dl case distinction applied rule case distinction

And obtained the following new goals

Rule argument

pos: right 1

Additional information

Used simplifier rules: py: ⊦ ispath(p, ino, m, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → ( py(user, p, tree, abs-files(files)) ↔ py(user, p, ino, dirs, files));%py-pw: ⊦ ispath(p, ino, m, dirs, files) ∧ py(user, p, ino, dirs, files) → pw(user, meta(ε, m, dirs, files));%py-last: ⊦ ispath(p, ino, m, dirs, files) ∧ py(user, p, ino, dirs, files) → px(user, meta(ε, m, dirs, files));%py-px: ⊦ ispath(p, ino, m, dirs, files) ∧ py(user, p, ino, dirs, files) → px(user, p, ino, dirs, files);% ⊦ parent(p + str ') = p; (s)%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]% ⊦ ino ∈ dirs → meta(ε, ino, dirs, files) = dirs[ino].meta; (s)%⊦ px(user, p, ino, dirs, files) → px-parent(user, p, ino, dirs, files); (s)% ⊦ mkdir(m, md, m0, m1, entries).meta = md; (s)