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Proof step 2 from proof Imp2 (previous step)

((P * P0))(H), P0 ⊆ P1 ⊦ ((P * P1))(H)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

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