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Proof step 415 from proof refine-link (previous step)

# links(ino2, dirs) = m1, # entries = m, dirs[ino2] = mkdir(# entries, md1, m1, m3, entries), files[entries0[str]] = mkfile(m0, md2, # links(entries0[str], dirs), content0), dirs[ino1] = mkdir(# entries0, md0, # links(ino1, dirs), m2, entries0), entries0[str] = dirs[ino].entries[str], dirs[ino2] = mkdir(m, md, m1, m3, entries1), root.dir?, root[q].dir?, root[q0].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q0, ROOT_INO, ino2, dirs, files), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, md1), px(user, md0), px(user, md1), px-parent(user, q0, ROOT_INO, dirs, files), px-parent(user, q, ROOT_INO, dirs, files), str ∈ entries0, entries0[str] ∈ files, ino1 ∈ dirs, ino2 ∈ dirs, ino ∈ dirs, str ∈ dirs[ino].entries, psynced → asynced0, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO, links(ino2, dirs) ≠ ∅ ∨ ino2 = ROOT_INO, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO ⊦ [fail#(; ; err); asynced := ?] ⟨posix_link#(q + str ', q0 + str0 ', user, abs-files(files), abs-of(of); err2, root; psynced)⟩ (abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err2), root[q + str '].dir?, str0 ∈ entries, entries0[str] ∈ dirs, str0 ∈ entries1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 416:
⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n, md, n0, n1, entries) → # entries = n
Proof step 417:
entries0[str] = dirs[ino].entries[str], dirs[ino1] = mkdir(# entries0, md0, # links(ino1, dirs), m2, entries0), files[entries0[str]] = mkfile(m0, md2, # links(entries0[str], dirs), content0), dirs[ino2] = mkdir(# entries1, md, # links(ino2, dirs), m3, entries1), root[q0].dir?, root[q].dir?, root.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), ispath(q0, ROOT_INO, ino2, dirs, files), of-cons(of, dirs, files), pw(user, md), px(user, md), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), px-parent(user, q0, ROOT_INO, dirs, files), str ∈ dirs[ino].entries, ino ∈ dirs, ino2 ∈ dirs, ino1 ∈ dirs, entries0[str] ∈ files, str ∈ entries0, ¬ root[q + str '].dir?, ¬ entries0[str] ∈ dirs, ¬ str0 ∈ entries1, psynced → asynced0, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO, links(ino2, dirs) ≠ ∅ ∨ ino2 = ROOT_INO, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [fail#(; ; err); asynced := ?] ⟨posix_link#(q + str ', q0 + str0 ', user, abs-files(files), abs-of(of); err2, root; psynced)⟩ (abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err2)

Rule argument

Additional information

Used simplifier rules: make-abs-fold-work: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n, md, n0, n1, entries) → # entries = n;%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)