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Proof step 7 from proof del-uni (previous step)

r0 ≠ r ∧ (r0 ∈ H0 ∨ r0 ∈ H1) ↔ r0 ∈ (H0 -- r) ∪ (H1 -- r), H0 ⊥ H1 ⊦ (r0 ≠ r ∧ (r0 ∈ H0 ∨ r0 ∈ H1) ↔ r0 ∈ (H0 -- r) ∪ (H1 -- r)) ∧ (r0 ≠ r ∧ (r0 ∈ H0 ∨ r0 ∈ H1) → (r0 ∈ H0 ⊃ H0[r0];H1[r0]) = ((H0 -- r) ∪ (H1 -- r))[r0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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