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Proof step 6 from proof sep-inj2-imp (previous step)

P0(H1), P2(H0), H1 ⊥ H0, ∀ H. P2(H) → P3(H), ∀ H. P0(H) → P1(H) ⊦ ((P1 * P3))(H1 ∪ H0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ P0(H0) ∧ P1(H1) ∧ H0 ⊥ H1 → ((P0 * P1))(H0 ∪ H1)
Proof step 8:
P0(H1), P2(H0), H1 ⊥ H0, ∀ H. P0(H) → P1(H), ∀ H. P2(H) → P3(H) ⊦ ((P1 * P3))(H1 ∪ H0), P1(H1) ∧ P3(H0) ∧ H1 ⊥ H0

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, P3, P1] flags: <all paths>

Additional information

Used terms: H0, H1, P3, P1