| fs[ri[inodekey(ino)]].directory, ro.inodes?, fo.inodes?, datakey(ino, n) ∈ ri, ro ⊆ dom ri, fo ⊆ dom fi, inodekey(ino) ∈ ri → ri[inodekey(ino)] ∈ fs ∧ node-closed(fs[ri[inodekey(ino)]], ri, fs, ro), datakey(ino, n) ∈ ri → ri[datakey(ino, n)] ∈ fs ∧ node-closed(fs[ri[datakey(ino, n)]], ri, fs, ro), ∀ adr. adr ∈ log → adr ∈ fs ∧ node-cons(fs[adr].key, fs[adr]), ∀ key. key ∈ ri → ri[key] ∈ fs ∧ node-closed(fs[ri[key]], ri, fs, ro), ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]) ⊦ dups(log), inodekey(0) ∈ ri |
fs[ri[inodekey(ino)]].directory, fo.inodes?, ro.inodes?, node-closed(fs[ri[datakey(ino, n)]], ri, fs, ro), datakey(ino, n) ∈ ri, ri[datakey(ino, n)] ∈ fs, fo ⊆ dom fi, ro ⊆ dom ri, inodekey(ino) ∈ ri → ri[inodekey(ino)] ∈ fs ∧ node-closed(fs[ri[inodekey(ino)]], ri, fs, ro), ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]), ∀ key. key ∈ ri → ri[key] ∈ fs ∧ node-closed(fs[ri[key]], ri, fs, ro), ∀ adr. adr ∈ log → adr ∈ fs ∧ node-cons(fs[adr].key, fs[adr]) ⊦ dups(log), inodekey(0) ∈ ri