∀ {R : Type u_1} [inst : CommRing R] {S : Submonoid R} {P : Type u_2} [inst_1 : CommRing P] [inst_2 : Algebra R P]
  {I J : Submodule R P} (motive : IsFractional S I → IsFractional S J → Prop) (x : IsFractional S I)
  (x_1 : IsFractional S J),
  (∀ (aI : R) (haI : aI ∈ S) (hI : ∀ b ∈ I, IsLocalization.IsInteger R (aI • b)) (aJ : R) (haJ : aJ ∈ S)
      (hJ : ∀ b ∈ J, IsLocalization.IsInteger R (aJ • b)), motive ⋯ ⋯) →
    motive x x_1