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Proof step 8 from proof del-uni (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 9:
r0 ∈ (H0 -- r) ∪ (H1 -- r), r0 ∈ H0, H0 ⊥ H1 ⊦ (r0 ∈ H0 ⊃ H0[r0];H1[r0]) = ((H0 -- r) ∪ (H1 -- r))[r0], r0 = r
Proof step 15:
r0 ∈ (H0 -- r) ∪ (H1 -- r), r0 ∈ H1, H0 ⊥ H1 ⊦ (r0 ∈ H0 ⊃ H0[r0];H1[r0]) = ((H0 -- r) ∪ (H1 -- r))[r0], r0 = r

Rule argument

pos: left 3

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