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Proof step 7 from proof replay-orphans-del (previous step)

key0 ∈ (ri ⊖ ro) -- key ↔ key0 ∈ (ri -- key) ⊖ ro ⊦ key ∈ ro, (key0 ≠ key ∧ key0 ∈ ri ⊖ ro ↔ key0 ∈ (ri -- key) ⊖ ro) ∧ (key0 ≠ key ∧ key0 ∈ ri ⊖ ro → (ri ⊖ ro)[key0] = ((ri -- key) ⊖ ro)[key0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
key0 ∈ ri, key0.data? → ¬ inodekey(key0.ino) ∈ ro ⊦ (ri ⊖ ro)[key0] = ((ri -- key) ⊖ ro)[key0], key0 = key, key ∈ ro, key0 ∈ ro

Rule argument

Additional information

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