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Proof step 29 from proof sep-ass (previous step)

P0(H1), P1(H2), P2(H), H2 ⊥ H, H1 ⊥ H2, H1 ⊥ H ⊦ (((P0 * P1) * P2))((H1 ∪ H2) ∪ H)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: split-union seq: ⊦ P0(H0) ∧ P1(H1) ∧ H0 ⊥ H1 → ((P0 * P1))(H0 ∪ H1) subst: [H1, H0, P1, P0] → [H, H1 ∪ H2, P2, P0 * P1] flags: <all paths>

Additional information

Used simplifier rules: split-union: ⊦ P0(H0) ∧ P1(H1) ∧ H0 ⊥ H1 → ((P0 * P1))(H0 ∪ H1);% ⊦ H1 ⊥ H2 → (H1 ∪ H2 ⊥ H0 ↔ H0 ⊥ H1 ∧ H0 ⊥ H2); (ss)% ⊦ H0 ⊥ H1 → H1 ⊥ H0; (s) Used terms: H, H1 ∪ H2, P2, P0 * P1