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Proof step 383 from proof refine-unlink (previous step)

⟨vfs_put_inode#(getinode(entries0[str], dirs1, files), of, asynced; err0, dirs, files)⟩ (err0 = ESUCCESS ∧ dirs = dirs1 ∧ files = files1), ⟨if ¬ is-open(entries0[str], of) ∧ ¬ ⌜entries0[str]⌝ ∈ (root0 -- (q + str ')).fids then fs := fs -- ⌜entries0[str]⌝ ⟩ (fs = fs0), # entries0 = m0 + 1, # links(entries0[str], dirs0) = m + 1, dirs0[ino1] = mkdir(m0 + 1, md0, # links(ino1, dirs0), m3, entries0), root0[q] = dnode(md0, sdt), files0[entries0[str]] = mkfile(m1, md1, m + 1, content0), dirs = dirs1, err0 = ESUCCESS, files = files0[entries0[str], mkfile(m1, md1, m, content0)], fs = abs-files(files0), entries0 ≠ ∅, ((ino1 => mkdir(m0, md0, # links(ino1, dirs0), m3, entries0 -- str) * abs|(root0, ROOT_INO, q, ino1) * abs(sdt, entries0)))(dirs1), (root0 -- (q + str ')).dir?, root0.dir?, dom of < ino0, afs-cons(dirs1, files1), afs-cons(dirs0, files0), fids-cons(root0 -- (q + str '), fs0, abs-of(of)), fids-cons(root0, abs-files(files0), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files0), of-cons(of, dirs1, files1), of-cons(of, dirs0, files0), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs0, files0), str ∈ sdt, ino1 ∈ dirs0, entries0[str] ∈ files0, q ∈ root0, str ∈ entries0, dirs1 ≡ dirs0[ino1, mkdir(m0, md0, # links(ino1, dirs0), m3, entries0 -- str)], ¬ root0[q + str '].dir?, ¬ abs(root0 -- (q + str '), ROOT_INO)(dirs1), ¬ entries0[str] ∈ dirs0, ¬ entries0[str] ∈ dirs1, psynced0 → asynced0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦

User applied rule weakening

And obtained the following new goals

Rule argument

poslist: left 1, left 2

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