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Proof step 2 from proof stability (previous step)

((P1 * {H} ))(H1), ((P0 * {H} ))(H0), P(H0), (P0 -⊗ P) * P1 ⊆ P ⊦ P(H1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
((P0 * {H} ))(H0), ((P1 * {H} ))(H1), P(H0), ∀ H. (((P0 -⊗ P) * P1))(H) → P(H) ⊦ P(H1)

Rule argument

Additional information

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