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Proof step 10 from proof ubifs-parent-dir (previous step)

fo.inodes?, ro.inodes?, node-closed(fs[ri[inodekey(ino)]], ri, fs, ro), node-closed(fs[ri[dentrykey(ino, str)]], ri, fs, ro), dentrykey(ino, str) ∈ ri, inodekey(ino) ∈ ri, ri[inodekey(ino)] ∈ fs, ri[dentrykey(ino, str)] ∈ fs, fo ⊆ dom fi, ro ⊆ dom ri, ∀ 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]) ⊦ fs[ri[inodekey(ino)]].directory, dups(log), inodekey(0) ∈ ri

Heuristic quantifier applied rule all left

And obtained the following new goals

Proof step 11:
ro.inodes?, fo.inodes?, node-closed(fs[ri[dentrykey(ino, str)]], ri, fs, ro), node-closed(fs[ri[inodekey(ino)]], ri, fs, ro), ri[dentrykey(ino, str)] ∈ fs, ri[inodekey(ino)] ∈ fs, inodekey(ino) ∈ ri, dentrykey(ino, str) ∈ ri, ro ⊆ dom ri, fo ⊆ dom fi, 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]]) ⊦ fs[ri[inodekey(ino)]].directory, dups(log), inodekey(0) ∈ ri

Rule argument

pos: left 11 terms: inodekey(ino)

Additional information

Used terms: inodekey(ino)