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Proof step 204 from proof inv-unlink (previous step)

# links(ino1, dirs) = dirs[ino1].nlink, # links(entries0[str], dirs) = files[entries0[str]].nlink, entries0[str] = dirs[ino1].entries[str], dirs[ino1] = mkdir(dirs[ino1].size, md0, dirs[ino1].nlink, dirs[ino1].nsubdirs, entries0), files[entries0[str]] = mkfile(m, md1, files[entries0[str]].nlink, content0), dom of < ino0, afs-cons(dirs, files), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), str ∈ dirs[ino1].entries, str ∈ entries0, entries0[str] ∈ files, ino1 ∈ dirs, ¬ entries0[str] ∈ dirs, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [fail#(; ; err); asynced := ?] ⟪vfs_put_inode#(mkinode(entries0[str], md1, false, files[entries0[str]].nlink, 0, m), of, asynced; err, dirs, files)⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 205:
# links(entries0[str], dirs) = m1, # links(ino1, dirs) = dirs[ino1].nlink, files[entries0[str]] = mkfile(m, md1, m1, content0), dirs[ino1] = mkdir(dirs[ino1].size, md0, dirs[ino1].nlink, dirs[ino1].nsubdirs, entries0), entries0[str] = dirs[ino1].entries[str], files[entries0[str]] = mkfile(m0, md, m1, content), dom of < ino0, afs-cons(dirs, files), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), ino1 ∈ dirs, entries0[str] ∈ files, str ∈ entries0, str ∈ dirs[ino1].entries, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [fail#(; ; err); asynced := ?] ⟪vfs_put_inode#(mkinode(entries0[str], md1, false, m1, 0, m), of, asynced; err, dirs, files)⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files)), entries0[str] ∈ dirs

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, md, m1, content]

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, md, m1, content