∀ {M : Type u_1} [inst : MulOneClass M] (s₁ : Submonoid M) (h₁ : s₁.MulSaturated)
  (motive : (x : SaturatedSubmonoid M) → { toSubmonoid := s₁, mulSaturated := h₁ }.toSubmonoid = x.toSubmonoid → Prop)
  (x : SaturatedSubmonoid M) (eq : { toSubmonoid := s₁, mulSaturated := h₁ }.toSubmonoid = x.toSubmonoid),
  (∀ (s₂ : Submonoid M) (h₂ : s₂.MulSaturated)
      (eq :
        { toSubmonoid := s₁, mulSaturated := h₁ }.toSubmonoid = { toSubmonoid := s₂, mulSaturated := h₂ }.toSubmonoid),
      motive { toSubmonoid := s₂, mulSaturated := h₂ } eq) →
    motive x eq