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Proof step 5 from proof replay-orphans-del (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
⊦ key ∈ ro, (key0 ≠ key ∧ key0 ∈ ri ⊖ ro ↔ key0 ∈ (ri -- key) ⊖ ro) ∧ (key0 ≠ key ∧ key0 ∈ ri ⊖ ro → (ri ⊖ ro)[key0] = ((ri -- key) ⊖ ro)[key0])

Rule argument

Additional information

Used simplifier rules: ⊦ key ≠ key0 → (ri -- key0)[key] = ri[key]; (s)% ⊦ key ∈ ri -- key0 ↔ key ≠ key0 ∧ key ∈ ri; (s)