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Proof step 10 from proof del-uni (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: at-uni seq: r ∈ H0 ∪ H1 ⊦ H0 ⊥ H1 → (H0 ∪ H1)[r] = (r ∈ H0 ⊃ H0[r];H1[r]) subst: [r, H1, H0] → [r0, H1 -- r, H0 -- r] flags: <all paths>

Additional information

Used simplifier rules: in-del: ⊦ r ∈ H -- r0 ↔ r ≠ r0 ∧ r ∈ H;%at-del: r ∈ H ⊦ r ≠ r0 → (H -- r0)[r] = H[r]; Used terms: r0, H1 -- r, H0 -- r