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Proof step 136 from proof refine-link (previous step)

entries = ∅ ↔ sdt = ∅, dirs[entries0[str]] = mkdir(# entries, md, # links(entries0[str], dirs), m1, entries), dirs[ino1] = mkdir(# entries0, md0, # links(ino1, dirs), m2, entries0), root[q + str '] = dnode(md1, sdt), root.dir?, root[q].dir?, root[q + str '].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), str ∈ entries0, ino1 ∈ dirs, entries0[str] ∈ dirs, psynced → asynced, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ⟨posix_link#(q + str ', path', user, abs-files(files), abs-of(of); err0, root; psynced)⟩ (abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ EISDIR = err0), path' = ε

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 137:
entries = ∅ ↔ sdt = ∅, dirs[entries0[str]] = mkdir(# entries, md, # links(entries0[str], dirs), m1, entries), dirs[ino1] = mkdir(# entries0, md0, # links(ino1, dirs), m2, entries0), root[q + str '] = dnode(md1, sdt), path' ≠ ε, root.dir?, root[q].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), str ∈ entries0, ino1 ∈ dirs, entries0[str] ∈ dirs, psynced → asynced, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ⟨posix_link#(q + str ', path', user, abs-files(files), abs-of(of); err0, root; psynced)⟩ (abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ EISDIR = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ dnode(md, sdt).dir?; (s)