{α : Type u} →
  {M : Matroid α} →
    {motive : M.InvariantCardinalRank → Sort u_1} →
      (t : M.InvariantCardinalRank) →
        ((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 ⋯) →
          motive t