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Proof step 38 from proof refine-close (previous step)

files[m] = mkfile(m1, md, m2, content), of0[fd] = mkfile(m, mode, m0), err = ESUCCESS, fs = abs-files(files), root.dir?, dom of0 < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of0)), of-cons(of0, dirs, files), fd ∈ of0, ¬ is-open(m, of0 -- fd), psynced → asynced ⊦ [afs_evict#(mkinode(m, md, false, m2, 0, m1), asynced; err, dirs, files)] ( of-cons(of0 -- fd, dirs, files) ∧ afs-cons(dirs, files) → ⟨ofh := abs-of(of0); posix_close#(fd, user, root; err0, fs, ofh)⟩ (ofh = abs-of(of0 -- fd) ∧ fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err0))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 39:
of0[fd] = mkfile(m, mode, m0), files[m] = mkfile(m1, md, m2, content), err = ESUCCESS, fs = abs-files(files), inode = mkinode(m, md, false, m2, 0, m1), root.dir?, dom of0 < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of0)), of-cons(of0, dirs, files), fd ∈ of0, psynced → asynced ⊦ [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] ( of-cons(of0 -- fd, dirs, files) ∧ afs-cons(dirs, files) → ⟨ofh := abs-of(of0); posix_close#(fd, user, root; err0, fs, ofh)⟩ (ofh = abs-of(of0 -- fd) ∧ fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err0)), is-open(m, of0 -- fd)

Rule argument

pos: right 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 };