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Proof step 11 from proof uni-com (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
r ∈ H1 ∪ H0, H0 ⊥ H1, r ∈ H1 ∨ r ∈ H0 ⊦ (r ∈ H1 ⊃ H1[r];H0[r]) = (H0 ∪ H1)[r]

Rule argument

Additional information

Used simplifier rules: disj-com-rw: ⊦ H0 ⊥ H1 → H1 ⊥ H0;