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Proof step 3 from proof overwrite-icache-empty (previous step)

⊦ ∀ ino. (ino ∈ files ⊕ ∅ ↔ ino ∈ files) ∧ (ino ∈ files ⊕ ∅ → (files ⊕ ∅)[ino] = files[ino])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
ino ∈ files ⊦ (files ⊕ ∅)[ino] = files[ino]

Rule argument

Additional information

Used simplifier rules: in-icache-overwrite: ⊦ ino ∈ files ⊕ icache ↔ ino ∈ files;