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Proof step 8 from proof and-split (previous step)

P(H1), P0(H0), P1(H0), precise(P), H1 ⊥ H0 ⊦ ((P * (P0 ∧ P1)))(H1 ∪ H0)

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] → [H0, H1, P0 ∧ P1, P] flags: <all paths>

Additional information

Used simplifier rules: and: ⊦ ((P0 ∧ P1))(H) ↔ P0(H) ∧ P1(H);%and-ass: ⊦ ((P0 ∧ P1) ∧ P2) = (P0 ∧ P1 ∧ P2);%and-com: ⊦ (P0 ∧ P1) = (P1 ∧ P0); Used terms: H0, H1, P0 ∧ P1, P