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Proof step 2 from proof ri-cons-del-orphans (previous step)

ri-cons(ri, fs) ⊦ ri-cons(ri ⊖ ro, fs)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
key ∈ ri, key.data? → ¬ inodekey(key.ino) ∈ ro, ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]) ⊦ key ∈ ro, (ri ⊖ ro)[key] ∈ fs ∧ key-cons(key, fs[(ri ⊖ ro)[key]])

Rule argument

Additional information

Used simplifier rules: ri-cons: ⊦ ri-cons(ri, fs) ↔ (∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]));%⊦ key ∈ ri ⊖ ks ↔ key ∈ ri ∧ ¬ key ∈ ks ∧ (key.data? → ¬ inodekey(key.ino) ∈ ks); (ws)