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Proof step 3 from proof precise-split-l (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ precise(P) ↔ (∀ H, H0, H1, H2. P(H) ∧ P(H0) ∧ H ⊥ H1 ∧ H0 ⊥ H2 ∧ H ∪ H1 = H0 ∪ H2 → H = H0)
Proof step 5:
((P0 * P1))(H0 ∪ H1), P0(H0), H0 ⊥ H1, ∀ H, H0, H1, H2. P0(H) ∧ P0(H0) ∧ H ⊥ H1 ∧ H0 ⊥ H2 ∧ H ∪ H1 = H0 ∪ H2 → H = H0 ⊦ P1(H1)

Rule argument

spec: <toplevel> name: precise seq: ⊦ precise(P) ↔ (∀ H, H0, H1, H2. P(H) ∧ P(H0) ∧ H ⊥ H1 ∧ H0 ⊥ H2 ∧ H ∪ H1 = H0 ∪ H2 → H = H0) subst: [P] → [P0] flags: <all paths>

Additional information

Used terms: P0