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Proof step 90 from proof refine-rmdir (previous step)

dirs[ino1] = mkdir(# entries, md, # links(ino1, dirs), m1, entries), root.dir?, root[q].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, md) ∨ ¬ pw(user, md) ⊦ ¬ py(user, q, ROOT_INO, dirs, files) ∧ ⟨err0 := EACCESS; if err0 = ESUCCESS then root := root -- (q + str '); psynced := ?⟩ (abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ EACCESS = err0)

Heuristic dl case distinction applied rule case distinction

And obtained the following new goals

Proof step 91:
⊦ ispath(p, ino, m, dirs, files) ∧ py(user, p, ino, dirs, files) → pw(user, meta(ε, m, dirs, files))
Proof step 92:
⊦ ispath(p, ino, m, dirs, files) ∧ py(user, p, ino, dirs, files) → px(user, meta(ε, m, dirs, files))
Proof step 93:
⊦ ispath(p, ino, m, dirs, files) ∧ py(user, p, ino, dirs, files) → px(user, p, ino, dirs, files)
Proof step 94:
dirs[ino1] = mkdir(# entries, md, # links(ino1, dirs), m1, entries), 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, md) ∨ ¬ pw(user, md) ⊦ ⟨err0 := EACCESS; if err0 = ESUCCESS then root := root -- (q + str '); psynced := ?⟩ (abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ EACCESS = err0)

Rule argument

pos: right 1

Additional information

Used simplifier rules: 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);% ⊦ 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)