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Proof step 581 from proof refine-unlink (previous step)

⟨afs_evict#(getinode(entries0[str], dirs, files), asynced; err, dirs, files)⟩ (err = err0 ∧ 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), err = ESUCCESS, files = files0[entries0[str], mkfile(m1, md1, m, content0)], fs = abs-files(files0), dirs ≠ dirs1, entries0 ≠ ∅, 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, dirs ≡ dirs0[ino1, mkdir(m0, md0, # links(ino1, dirs0), m3, entries0 -- str)], ¬ root[q + str '].dir?, ¬ is-open(entries0[str], of), ¬ entries0[str] ∈ dirs, ¬ entries0[str] ∈ dirs0, ¬ ino1 ∈ dirs, psynced → asynced0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ⟨posix_unlink#(q + str ', user, abs-of(of); err1, root, fs; psynced)⟩ (fs = abs-files(files1) ∧ abs(root, ROOT_INO)(dirs1) ∧ (psynced → asynced) ∧ err0 = err1)

User applied rule call left

And obtained the following new goals

Proof step 582:
⟨if pre-evict(inode, dirs, files) then {err := ESUCCESS; let ino = inode.ino in if ino ∈ dirs then if dirs[ino].nlink = 0 then dirs := dirs -- ino else if files[ino].nlink = 0 then files := files -- ino} else abort⟩ (err = err0 ∧ 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), err = ESUCCESS, files = files0[entries0[str], mkfile(m1, md1, m, content0)], fs = abs-files(files0), inode = getinode(entries0[str], dirs, files), 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, entries0[str] ∈ files0, str ∈ entries0, dirs ≡ dirs0[ino1, mkdir(m0, md0, # links(ino1, dirs0), m3, entries0 -- str)], psynced → asynced0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ⟨posix_unlink#(q + str ', user, abs-of(of); err1, root, fs; psynced)⟩ (fs = abs-files(files1) ∧ abs(root, ROOT_INO)(dirs1) ∧ (psynced → asynced) ∧ err0 = err1), dirs = dirs1, entries0 = ∅, root[q + str '].dir?, is-open(entries0[str], of), entries0[str] ∈ dirs, entries0[str] ∈ dirs0, ino1 ∈ dirs

Rule argument

pos: left 1

Additional information

Used simplifier rules: afs_evict#(INODE, ASYNCED; ERR, DIRS, FILES) {if pre-evict(INODE, DIRS, FILES) then {ERR := ESUCCESS; let INO = INODE.ino in if INO ∈ DIRS then if DIRS[INO].nlink = 0 then DIRS := DIRS -- INO else if FILES[INO].nlink = 0 then FILES := FILES -- INO} else abort };