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Proof step 71 from proof refine-open (previous step)

isdir ↔ false, root[path].dir? ↔ ino0 ∈ dirs, getinode(ino, dirs, files).directory ↔ isdir, err = ESUCCESS, err1 = err, err2 = err3, err3 = ESUCCESS, fd = ino1, ino = ino0, ofh = abs-of(of), root.dir?, dom of[ino2, mkfile(ino0, mode, 0)] < ino2 + 1, 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[ino2, mkfile(ino0, mode, 0)], dirs, files), of-cons(of, dirs, files), pre-iget(ino, dirs, files), px-parent(user, path, ROOT_INO, dirs, files), psynced → asynced ⊦ ⟨posix_open#(path, mode, user, root, abs-files(files); ino1, err0, ofh)⟩ (ofh = abs-of(of[ino2, mkfile(ino0, mode, 0)]) ∧ (psynced → asynced) ∧ ino2 = ino1 ∧ err1 = err0), (mode = MODE_R ∨ mode = MODE_RW) ∧ ¬ pr(user, getinode(ino, dirs, files).meta), (mode = MODE_W ∨ mode = MODE_RW) ∧ ¬ pw(user, getinode(ino, dirs, files).meta)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 72:
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[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, ¬ root[path].dir?, ¬ ino0 ∈ dirs, psynced → asynced ⊦ ⟨posix_open#(path, mode, user, root, abs-files(files); ino1, err0, ofh)⟩ (ofh = abs-of(of[ino1, mkfile(ino0, mode, 0)]) ∧ (psynced → asynced) ∧ ino2 = ino1 ∧ ESUCCESS = err0), (mode = MODE_R ∨ mode = MODE_RW) ∧ ¬ pr(user, files[ino0].meta), (mode = MODE_W ∨ mode = MODE_RW) ∧ ¬ pw(user, files[ino0].meta)

Rule argument

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)%path-in-dirs: p ≠ ε ⊦ ispath(p, n, m, dirs, files) → n ∈ dirs; (forward) from specification afs-base% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ px-parent(user, ε, ino, dirs, files); (s)% ⊦ tree[ε] = tree; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ ns < n → ns < n + 1; (s)% ⊦ ns ++ n < n + 1 ↔ ns < n + 1; (s)% ⊦ dom of[fd, file] = dom of ++ fd; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)% ⊦ pre-iget(ino, dirs, files) ↔ valid-ino(ino, dirs, files); (s)%⊦ getinode(ino, dirs, files) = (ino ∈ dirs ⊃ mkinode (ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ); (s)