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Proof step 113 from proof refine-open (previous step)

root[path].dir? ↔ ino0 ∈ dirs, fd = ino1, ofh = abs-of(of), root.dir?, dom of < ino2, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), px-parent(user, path, ROOT_INO, dirs, files), ⌊err0⌋ , psynced → asynced, ino0 ∈ dirs ∨ ino0 ∈ files ⊦ ⟨posix_open#(path, mode, user, root, abs-files(files); ino1, err2, ofh)⟩ (ofh = abs-of(of) ∧ (psynced → asynced) ∧ fd = ino1 ∧ err0 = err2)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 114:
root[path].dir? ↔ ino0 ∈ dirs, err0 = err2, fd = ino1, fd0 = ino1, fs = abs-files(files), ofh = abs-of(of), root.dir?, dom of < ino2, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), px-parent(user, path, ROOT_INO, dirs, files), ⌊err⌋ , psynced → asynced, ino0 ∈ dirs ∨ ino0 ∈ files ⊦ ⟨choose err with pre-open(path, mode, err, user, root, fs, ofh) in err0 := err; if err0 = ESUCCESS then let fid = root[path].fid in choose n with ¬ n ∈ ofh in {ofh[n] := mkfh(fid, mode, 0); fd := n}⟩ (ofh = abs-of(of) ∧ (psynced → asynced) ∧ fd0 = fd ∧ err = err0)

Rule argument

pos: right 1

Additional information

Used simplifier rules: posix_open#(PATH, MODE, USER, ROOT, FS; FD, ERR, OFH) {choose E with pre-open(PATH, MODE, E, USER, ROOT, FS, OFH) in ERR := E; if ERR = ESUCCESS then let FID = ROOT[PATH].fid in choose N with ¬ N ∈ OFH in {OFH[N] := mkfh(FID, MODE, 0); FD := N} };