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Proof step 7 from proof dels-ignore-data (previous step)

key ∈ (ri -- datakey(ino, n)) ⊖ ro ↔ key ∈ ri ⊖ ro, inodekey(ino) ∈ ro ⊦ # ro = 0, ro = ∅, (key ∈ (ri -- datakey(ino, n)) ⊖ ro ↔ key ∈ ri ⊖ ro) ∧ (key ∈ (ri -- datakey(ino, n)) ⊖ ro → ((ri -- datakey(ino, n)) ⊖ ro)[key] = (ri ⊖ ro)[key])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
inodekey(ino) ∈ ro, key ∈ ri, key.data? → ¬ inodekey(key.ino) ∈ ro ⊦ # ro = 0, ((ri -- datakey(ino, n)) ⊖ ro)[key] = (ri ⊖ ro)[key], key = datakey(ino, n), ro = ∅, key ∈ ro

Rule argument

Additional information

Used simplifier rules: in-dels-ro: ⊦ key ∈ ri ⊖ ks ↔ key ∈ ri ∧ ¬ key ∈ ks ∧ (key.data? → ¬ inodekey(key.ino) ∈ ks);% ⊦ key ∈ ri -- key0 ↔ key ≠ key0 ∧ key ∈ ri; (s)