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Proof step 5 from proof del-notin (previous step)

⊦ r ∈ H, ∀ r0. (r0 ∈ H -- r ↔ r0 ∈ H) ∧ (r0 ∈ H -- r → (H -- r)[r0] = H[r0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: in-del: ⊦ r ∈ H -- r0 ↔ r ≠ r0 ∧ r ∈ H;