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Proof step 312 from proof refine-unlink (previous step)

⟨vfs_put_inode#(getinode(entries0[str], dirs1, files), of, asynced; err3, dirs, files)⟩ (err3 = err2 ∧ 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, err0 = err2, err3 = ESUCCESS, fid = root0[q + str '].fid, files = files0[entries0[str], mkfile(m1, md1, m, content0)], fs = abs-files(files0), root = root0 -- (q + str '), root0[q].dir?, root0.dir?, dom of < ino0, abs(root0, ROOT_INO)(dirs0), afs-cons(dirs0, files0), afs-cons(dirs1, files1), fids-cons(root0, abs-files(files0), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files0), of-cons(of, dirs0, files0), of-cons(of, dirs1, files1), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs0, files0), str ∈ entries0, ino1 ∈ dirs0, entries0[str] ∈ files0, dirs1 ≡ dirs0[ino1, mkdir(m0, md0, # links(ino1, dirs0), m3, entries0 -- str)], psynced → asynced0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ⟨if ¬ fid ∈ abs-of(of).fids ∧ ¬ fid ∈ root.fids then fs := fs -- fid; psynced := ?⟩ (root.dir? ∧ fids-cons(root, fs, abs-of(of)) → fs = abs-files(files1) ∧ abs(root, ROOT_INO)(dirs1) ∧ (psynced → asynced) ∧ err2 = err0), entries0 = ∅, root0[q + str '].dir?, entries0[str] ∈ dirs0, entries0[str] ∈ dirs1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 313:
⊦ ispath(p, ino, m, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → p ∈ tree ∧ (tree[p].dir? ↔ m ∈ dirs)
Proof step 314:
⊦ 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] ∈ dirs ↔ tree[p + str '].dir?)
Proof step 315:
⊦ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (p ∈ tree ↔ ispath(p, ino, dirs, files))
Proof step 316:
⟨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), entries0 ≠ ∅, root0[q].dir?, root0.dir?, dom of < ino0, abs(root0, ROOT_INO)(dirs0), afs-cons(dirs0, files0), afs-cons(dirs1, files1), fids-cons(root0, abs-files(files0), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files0), of-cons(of, dirs0, files0), of-cons(of, dirs1, files1), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs0, files0), str ∈ entries0, ino1 ∈ dirs0, entries0[str] ∈ files0, dirs1 ≡ dirs0[ino1, mkdir(m0, md0, # links(ino1, dirs0), m3, entries0 -- str)], ¬ root0[q + str '].dir?, ¬ entries0[str] ∈ dirs0, ¬ entries0[str] ∈ dirs1, psynced → asynced0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ⟨if ¬ root0[q + str '].fid ∈ abs-of(of).fids ∧ ¬ root0[q + str '].fid ∈ (root0 -- (q + str ')).fids then fs := fs -- root0[q + str '].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))

Rule argument

Additional information

Used simplifier rules: path-in: ⊦ ispath(p, ino, m, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → p ∈ tree ∧ (tree[p].dir? ↔ m ∈ dirs);%dir-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] ∈ dirs ↔ tree[p + str '].dir?);%path-in-eq: ⊦ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (p ∈ tree ↔ ispath(p, ino, dirs, files));% ⊦ ispath(p, n, m, dirs, files) → ispath(p, n, dirs, files); (s)