∀ {σ₁ : Type u_1} {σ₂ : Type u_2} {f₁ : σ₁ → Option σ₁} {f₂ : σ₂ → Option σ₂} {tr : σ₁ → σ₂ → Prop},
  StateTransition.Respects f₁ f₂ tr →
    ∀ {a₁ : σ₁} {a₂ : σ₂}, tr a₁ a₂ → ((StateTransition.eval f₂ a₂).Dom ↔ (StateTransition.eval f₁ a₁).Dom)