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Proof step 16 from proof replay-orphans-inode (previous step)

⊦ key = inodekey(ino), inodekey(ino) ∈ ro, (key ∈ ri ⊖ ro ↔ key ∈ ri[inodekey(ino), adr] ∧ ¬ key ∈ ro ∧ (key.data? → ¬ inodekey(key.ino) ∈ ro)) ∧ (key ∈ ri ⊖ ro → (ri ⊖ ro)[key] = (ri[inodekey(ino), adr] ⊖ ro)[key])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
⊦ key = inodekey(ino), inodekey(ino) ∈ ro, (key ∈ ri ⊖ ro → key ∈ ri ∧ ¬ key ∈ ro ∧ (key.data? → ¬ inodekey(key.ino) ∈ ro)) ∧ (key ∈ ri ⊖ ro → (ri ⊖ ro)[key] = (ri[inodekey(ino), adr] ⊖ ro)[key])

Rule argument

Additional information

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