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Proof step 5 from proof uni-ass (previous step)

H0 ⊥ H1, H1 ⊥ H, H ⊥ H0 ⊦ ∀ r. (r ∈ (H0 ∪ H1) ∪ H ↔ r ∈ H0 ∪ H1 ∪ H) ∧ (r ∈ (H0 ∪ H1) ∪ H → ((H0 ∪ H1) ∪ H)[r] = (H0 ∪ H1 ∪ H)[r])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information