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Proof step 2 from proof sep-inj2-imp (previous step)

P0 ⊆ P1, P2 ⊆ P3 ⊦ P0 * P2 ⊆ P1 * P3

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
((P0 * P2))(H), ∀ H. P2(H) → P3(H), ∀ H. P0(H) → P1(H) ⊦ ((P1 * P3))(H)

Rule argument

Additional information

Used simplifier rules: Imp: ⊦ P0 ⊆ P1 ↔ (∀ H. P0(H) → P1(H));