{α : Type u} →
  {M : Matroid α} →
    {motive : M.InvariantCardinalRank → Sort u_1} →
      ((forall_card_isBasis_diff :
            ∀ ⦃I J X : Set α⦄, M.IsBasis I X → M.IsBasis J X → Cardinal.mk ↑(I \ J) = Cardinal.mk ↑(J \ I)) →
          motive ⋯) →
        (t : M.InvariantCardinalRank) → motive t