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Proof step 491 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), # links(entries0[str], dirs0) = m + 1, # entries0 = m0 + 1, dirs0[ino1] = mkdir(m0 + 1, md0, # links(ino1, dirs0), m3, entries0), files0[entries0[str]] = mkfile(m1, md1, m + 1, content0), root0[q + str '] = fnode(fid), dirs = dirs1, err0 = ESUCCESS, files = files0[entries0[str], mkfile(m1, md1, m, content0)], fs = abs-files(files0), root0.dir?, root0[q].dir?, dom of < ino0, abs(root0, ROOT_INO)(dirs0), afs-cons(dirs1, files1), afs-cons(dirs0, files0), 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), entries0[str] ∈ files0, str ∈ entries0, ino1 ∈ dirs0, dirs1 ≡ dirs0[ino1, mkdir(m0, md0, # links(ino1, dirs0), m3, entries0 -- str)], psynced → asynced0 ⊦ ⟨if ¬ fid ∈ abs-of(of).fids ∧ ¬ fid ∈ (root0 -- (q + str ')).fids then fs := fs -- fid; psynced := ?⟩ ( (root0 -- (q + str ')).dir? ∧ fids-cons(root0 -- (q + str '), fs, abs-of(of)) → fs = abs-files(files1) ∧ abs(root0 -- (q + str '), ROOT_INO)(dirs1) ∧ (psynced → asynced)), # links(ino1, dirs0) = 0, entries0 = ∅, ino1 = ROOT_INO, links(ino1, dirs0) = ∅, root0[q + str '].dir?, entries0[str] ∈ dirs0, ino1 ∈ dirs1, entries0[str] ∈ dirs1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 492:
⊦ ispath(p, ino, m, dirs, files) ∧ px-parent(user, p, ino, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) ∧ m ∈ dirs ∧ dirs[m] = mkdir(m0, md, n0, n1, entries) ∧ str ∈ entries ∧ entries[str] ∈ files → (tree[p + str '] = fnode(fid) ↔ fid = ⌜entries[str]⌝ )
Proof step 493:
⊦ ⌜ino⌝ ∈ abs-of(of).fids ↔ is-open(ino, of)
Proof step 494:
⟨vfs_put_inode#(getinode(entries0[str], dirs1, files), of, asynced; err0, dirs, files)⟩ (err0 = ESUCCESS ∧ dirs = dirs1 ∧ files = files1), # links(entries0[str], dirs0) = m + 1, # entries0 = m0 + 1, dirs0[ino1] = mkdir(m0 + 1, md0, # links(ino1, dirs0), m3, entries0), 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), # links(ino1, dirs0) ≠ 0, entries0 ≠ ∅, ino1 ≠ ROOT_INO, links(ino1, dirs0) ≠ ∅, root0.dir?, root0[q].dir?, dom of < ino0, abs(root0, ROOT_INO)(dirs0), afs-cons(dirs1, files1), afs-cons(dirs0, files0), 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), entries0[str] ∈ files0, str ∈ entries0, ino1 ∈ dirs0, dirs1 ≡ dirs0[ino1, mkdir(m0, md0, # links(ino1, dirs0), m3, entries0 -- str)], ¬ root0[q + str '].dir?, ¬ entries0[str] ∈ dirs0, ¬ ino1 ∈ dirs1, ¬ entries0[str] ∈ dirs1, psynced → asynced0 ⊦ ⟨if ¬ is-open(entries0[str], of) ∧ ¬ ⌜entries0[str]⌝ ∈ (root0 -- (q + str ')).fids then fs := fs -- ⌜entries0[str]⌝ ; psynced := ?⟩ ( (root0 -- (q + str ')).dir? ∧ fids-cons(root0 -- (q + str '), fs, abs-of(of)) → fs = abs-files(files1) ∧ abs(root0 -- (q + str '), ROOT_INO)(dirs1) ∧ (psynced → asynced))

Rule argument

Additional information

Used simplifier rules: fid-ino-entry: ⊦ ispath(p, ino, m, dirs, files) ∧ px-parent(user, p, ino, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) ∧ m ∈ dirs ∧ dirs[m] = mkdir(m0, md, n0, n1, entries) ∧ str ∈ entries ∧ entries[str] ∈ files → (tree[p + str '] = fnode(fid) ↔ fid = ⌜entries[str]⌝ );%of: ⊦ ⌜ino⌝ ∈ abs-of(of).fids ↔ is-open(ino, of);%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]