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Proof step 50 from proof refine-close (previous step)

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

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 51:
# links(m, dirs) = 0, of0[fd] = mkfile(m, mode, m0), files[m] = mkfile(m1, md, 0, content), fs = abs-files(files), ofh = abs-of(of0), root.dir?, dom of0 < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), afs-cons(dirs, files -- m), fids-cons(root, abs-files(files), abs-of(of0)), of-cons(of0 -- fd, dirs, files -- m), of-cons(of0, dirs, files), fd ∈ of0, m ∈ files, psynced → asynced ⊦ ⟨choose err with pre-close(fd, err, user, root, fs, ofh) in err0 := err; if err0 = ESUCCESS then let fid = ofh[fd].fid in {ofh := ofh -- fd; if ¬ fid ∈ ofh.fids ∧ ¬ fid ∈ root.fids then fs := fs -- fid}⟩ (ofh = abs-of(of0 -- fd) ∧ fs = abs-files(files -- m) ∧ (psynced → asynced) ∧ ESUCCESS = err0), m = ROOT_INO, is-open(m, of0 -- fd)

Rule argument

pos: right 1

Additional information

Used simplifier rules: posix_close#(FD, USER, ROOT; ERR, FS, OFH) {choose E with pre-close(FD, E, USER, ROOT, FS, OFH) in ERR := E; if ERR = ESUCCESS then let FID = OFH[FD].fid in {OFH := OFH -- FD; if ¬ FID ∈ OFH.fids ∧ ¬ FID ∈ ROOT.fids then FS := FS -- FID} };