{motive : Simps.ProjectionRule → Sort u} →
  (t : Simps.ProjectionRule) →
    ((oldName : Lean.Name) →
        (oldStx : Lean.Syntax) →
          (newName : Lean.Name) →
            (newStx : Lean.Syntax) → motive (Simps.ProjectionRule.rename oldName oldStx newName newStx)) →
      ((a : Lean.Name) → (a_1 : Lean.Syntax) → motive (Simps.ProjectionRule.add a a_1)) →
        ((a : Lean.Name) → (a_1 : Lean.Syntax) → motive (Simps.ProjectionRule.erase a a_1)) →
          ((a : Lean.Name) → (a_1 : Lean.Syntax) → motive (Simps.ProjectionRule.prefix a a_1)) → motive t