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Proof step 7 from proof sep-partial-mp-2 (previous step)

((P0 * (P0 * P2 -* P1)))(H1), ((P0 * P * (P0 * P2 -* P1)))(H0 ∪ H1), P(H0), H0 ⊥ H1, ∀ P0. ((P * P0))(H0 ∪ H1) → (∃ H2, H3. H2 ⊥ H3 ∧ H2 ∪ H3 = H0 ∪ H1 ∧ P(H2) ∧ P0(H3)) ⊦ ((P * (P2 -* P1)))(H0 ∪ H1)

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] → [H1, H0, P2 -* P1, P] flags: <all paths>

Additional information

Used simplifier rules: sep-ass: ⊦ (P0 * P1) * P2 = P0 * P1 * P2;%sep-com: ⊦ P0 * P1 = P1 * P0;%sep-partial-mp: ⊦ ((P0 * (P0 * P2 -* P1)))(H) → ((P2 -* P1))(H); Used terms: H1, H0, P2 -* P1, P