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Proof step 562 from proof refine-unlink (previous step)

⟨vfs_put_inode#(getinode(entries0[str], dirs1, files), of, asynced; err3, dirs, files)⟩ (err3 = err2 ∧ dirs = dirs1 ∧ files = files1), # entries0 = m0 + 1, # links(entries0[str], dirs0) = m + 1, files0[entries0[str]] = mkfile(m1, md1, m + 1, content0), dirs0[ino1] = mkdir(m0 + 1, md0, # links(ino1, dirs0), m3, entries0), dirs = dirs1, err3 = ESUCCESS, files = files0[entries0[str], mkfile(m1, md1, m, content0)], # links(ino1, dirs0) ≠ 0, entries0 ≠ ∅, err2 ≠ ESUCCESS, ino1 ≠ ROOT_INO, links(ino1, dirs0) ≠ ∅, root[q].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs0, files0), afs-cons(dirs1, files1), fids-cons(root, abs-files(files0), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files0), of-cons(of, dirs0, files0), of-cons(of, dirs1, files1), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs0, files0), ino1 ∈ dirs0, str ∈ entries0, entries0[str] ∈ files0, dirs1 ≡ dirs0[ino1, mkdir(m0, md0, # links(ino1, dirs0), m3, entries0 -- str)], ¬ root[q + str '].dir?, ¬ entries0[str] ∈ dirs0, ¬ ino1 ∈ dirs1, ¬ entries0[str] ∈ dirs1, psynced → asynced0 ⊦ ⟨psynced := ?⟩ (abs-files(files0) = abs-files(files1) ∧ abs(root, ROOT_INO)(dirs1) ∧ (psynced → asynced))

User applied rule call left

And obtained the following new goals

Proof step 563:
⟨if err = ESUCCESS ∧ ¬ is-open(p_inode.ino, of) then afs_evict#(p_inode, asynced; err, dirs, files)⟩ (err = err2 ∧ dirs = dirs1 ∧ files = files1), # links(entries0[str], dirs0) = m + 1, # entries0 = m0 + 1, dirs0[ino1] = mkdir(m0 + 1, md0, # links(ino1, dirs0), m3, entries0), files0[entries0[str]] = mkfile(m1, md1, m + 1, content0), dirs = dirs1, err = err3, err3 = ESUCCESS, files = files0[entries0[str], mkfile(m1, md1, m, content0)], p_inode = getinode(entries0[str], dirs1, files), root.dir?, root[q].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs1, files1), afs-cons(dirs0, files0), fids-cons(root, abs-files(files0), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files0), of-cons(of, dirs1, files1), of-cons(of, dirs0, files0), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs0, files0), entries0[str] ∈ files0, ino1 ∈ dirs0, str ∈ entries0, dirs1 ≡ dirs0[ino1, mkdir(m0, md0, # links(ino1, dirs0), m3, entries0 -- str)], psynced → asynced0 ⊦ ⟨psynced := ?⟩ (abs-files(files0) = abs-files(files1) ∧ abs(root, ROOT_INO)(dirs1) ∧ (psynced → asynced)), # links(ino1, dirs0) = 0, entries0 = ∅, err2 = ESUCCESS, ino1 = ROOT_INO, links(ino1, dirs0) = ∅, root[q + str '].dir?, entries0[str] ∈ dirs0, ino1 ∈ dirs1, entries0[str] ∈ dirs1

Rule argument

pos: left 1

Additional information

Used simplifier rules: vfs_put_inode#(DEL_INODE, OF, ASYNCED; ERR, DIRS, FILES) {if ERR = ESUCCESS ∧ ¬ is-open(DEL_INODE.ino, OF) then afs_evict#(DEL_INODE, ASYNCED; ERR, DIRS, FILES) };