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Proof step 12 from proof del-uni (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: in-uni: ⊦ H0 ⊥ H1 → (r ∈ H0 ∪ H1 ↔ r ∈ H0 ∨ r ∈ H1);%in-del: ⊦ r ∈ H -- r0 ↔ r ≠ r0 ∧ r ∈ H;