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Proof step 15 from proof del-uni (previous step)

r0 ∈ (H0 -- r) ∪ (H1 -- r), r0 ∈ H1, H0 ⊥ H1 ⊦ (r0 ∈ H0 ⊃ H0[r0];H1[r0]) = ((H0 -- r) ∪ (H1 -- r))[r0], r0 = r

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: disj-r: ⊦ r ∈ H1 ∧ H0 ⊥ H1 → (r ∈ H0 ↔ false);