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Proof step 412 from proof refine-link (previous step)

# links(entries0[str], dirs) = files[entries0[str]].nlink, # entries = dirs[ino2].size, # links(ino2, dirs) = dirs[ino2].nlink, entries0[str] = dirs[ino].entries[str], dirs[ino1] = mkdir(# entries0, md0, # links(ino1, dirs), m2, entries0), files[entries0[str]] = mkfile(m, md, files[entries0[str]].nlink, content), dirs[ino2] = mkdir(# entries, md1, dirs[ino2].nlink, dirs[ino2].nsubdirs, entries), 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, md1), px(user, md1), 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?, ¬ str0 ∈ dirs[ino2].entries, ¬ entries0[str] ∈ dirs, ¬ str0 ∈ entries, 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)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 413:
# links(ino2, dirs) = dirs[ino2].nlink, # entries = dirs[ino2].size, # links(entries0[str], dirs) = m1, dirs[ino2] = mkdir(# entries, md1, dirs[ino2].nlink, dirs[ino2].nsubdirs, entries), files[entries0[str]] = mkfile(m, md, m1, content), dirs[ino1] = mkdir(# entries0, md0, # links(ino1, dirs), m2, entries0), entries0[str] = dirs[ino].entries[str], files[entries0[str]] = mkfile(m0, md2, m1, content0), 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 ∈ dirs[ino2].entries, entries0[str] ∈ dirs, str0 ∈ entries

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [files[entries0[str]], m0, md2, m1, content0]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: files[entries0[str]], m0, md2, m1, content0