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Proof step 98 from proof refine-open (previous step)

files[ino0] = mkfile(m, md, # links(ino0, dirs), content), ofh = abs-of(of), root.dir?, 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[ino2, mkfile(ino0, mode, 0)], dirs, files), of-cons(of, dirs, files), px-parent(user, path, ROOT_INO, dirs, files), ROOT_INO ∈ dirs, ino0 ∈ files, ino2 ∈ of, ¬ root[path].dir?, ¬ ino0 ∈ dirs, psynced → asynced, ∀ n. n ∈ of → n < ino2 ⊦ ∃ err1. pre-open(path, mode, err1, user, root, abs-files(files), ofh) ∧ ⟨err := err1; if err = ESUCCESS then let fid = ⌜ino0⌝ in choose n with ¬ n ∈ ofh in {ofh[n] := mkfh(fid, mode, 0); fd := n}⟩ (ofh = abs-of(of[fd, mkfile(ino0, mode, 0)]) ∧ (psynced → asynced) ∧ ino2 = fd ∧ ESUCCESS = err), (mode = MODE_R ∨ mode = MODE_RW) ∧ ¬ pr(user, md), (mode = MODE_W ∨ mode = MODE_RW) ∧ ¬ pw(user, md)

Proof step 98 from proof refine-open (previous step)

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

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