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Proof step 9 from proof ubifs-parent-in (previous step)

ro.inodes?, fo.inodes?, node-closed(fs[ri[dentrykey(ino, str)]], ri, fs, ro), ri[dentrykey(ino, str)] ∈ fs, dentrykey(ino, str) ∈ ri, ro ⊆ dom ri, fo ⊆ dom fi, dentrykey(ino, str) ∈ ri → ri[dentrykey(ino, str)] ∈ fs ∧ key-cons(dentrykey(ino, str), fs[ri[dentrykey(ino, str)]]), ∀ 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(ino) ∈ ri, inodekey(0) ∈ ri

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
fs[ri[dentrykey(ino, str)]].key = dentrykey(ino, str), fs[ri[dentrykey(ino, str)]].dentry?, fo.inodes?, ro.inodes?, node-closed(fs[ri[dentrykey(ino, str)]], ri, fs, ro), dentrykey(ino, str) ∈ ri, 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]) ⊦ dups(log), inodekey(0) ∈ ri, inodekey(ino) ∈ ri

Rule argument

Additional information

Used simplifier rules: dentrykey-cons: ⊦ key-cons(dentrykey(ino, str), nd) ↔ nd.dentry? ∧ nd.key = dentrykey(ino, str);