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Proof step 8 from proof precise-split-r (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
precise(P0) ⊦ P0(H0) ∧ H0 ⊥ H1 → (((P0 * P1))(H0 ∪ H1) ↔ P1(H1))

Rule argument

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

Additional information

Used simplifier rules: ⊦ H0 ⊥ H1 → H1 ⊥ H0; (s) Used terms: H0, H1, P0, P1