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Proof step 11 from proof ubifs-file-notdir (previous step)

fs[ri[inodekey(ino)]].directory, ro.inodes?, fo.inodes?, node-closed(fs[ri[datakey(ino, n)]], ri, fs, ro), ri[datakey(ino, n)] ∈ fs, 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), inodekey(ino) ∈ ri → ri[inodekey(ino)] ∈ fs ∧ key-cons(inodekey(ino), fs[ri[inodekey(ino)]]), ∀ 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
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), inodekey(ino) ∈ ri → ri[inodekey(ino)] ∈ fs ∧ fs[ri[inodekey(ino)]].inode? ∧ fs[ri[inodekey(ino)]].key = inodekey(ino), ∀ 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

Rule argument

Additional information

Used simplifier rules: inodekey-cons: ⊦ key-cons(inodekey(ino), nd) ↔ nd.inode? ∧ nd.key = inodekey(ino) ∧ ino ≠ 0;