{R : Type u_1} →
  [inst : Semiring R] →
    {P : Type u_2} →
      [inst_1 : AddCommMonoid P] →
        [inst_2 : Module R P] →
          {motive : Module.Projective R P → Sort u} →
            ((out : ∃ s, Function.LeftInverse ⇑(Finsupp.linearCombination R id) ⇑s) → motive ⋯) →
              (t : Module.Projective R P) → motive t