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Proof step 5 from proof and-split (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
precise(P0) ⊦ P0(H0) ∧ H0 ⊥ H1 → (((P0 * P1))(H0 ∪ H1) ↔ P1(H1))
Proof step 7:
P(H1), P0(H0), P1(H0), precise(P), H1 ⊥ H0 ⊦ ((P * (P0 ∧ P1)))(H1 ∪ H0)

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, P1, P] flags: <all paths>

Additional information

Used terms: H0, H1, P1, P