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Proof step 3 from proof precise-sep (previous step)

precise(P1), precise(P0) ⊦ precise(P0 * P1)

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:
precise(P0), precise(P1) ⊦ ∀ H, H0, H1, H2. ((P0 * P1))(H) ∧ ((P0 * P1))(H0) ∧ H ⊥ H1 ∧ H0 ⊥ H2 ∧ H ∪ H1 = H0 ∪ H2 → H = H0

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 * P1] flags: <all paths>

Additional information

Used terms: P0 * P1