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Proof step 3 from proof ri-cons-del-orphans (previous step)

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]])

User applied rule all left

And obtained the following new goals

Proof step 4:
key ∈ ri, key.data? → ¬ inodekey(key.ino) ∈ ro, 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

pos: left 3 terms: key abort: F discard: T computed: T

Additional information

Used terms: key