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Proof step 3 from proof and-weaken (previous step)

∀ H. P1(H) → P0(H) ⊦ ((P0 ∧ P1))(H) ↔ P1(H)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
P1(H), ∀ H. P1(H) → P0(H) ⊦ P0(H)

Rule argument

Additional information

Used simplifier rules: and: ⊦ ((P0 ∧ P1))(H) ↔ P0(H) ∧ P1(H);%and-ass: ⊦ ((P0 ∧ P1) ∧ P2) = (P0 ∧ P1 ∧ P2);%and-com: ⊦ (P0 ∧ P1) = (P1 ∧ P0);