{X : Type u_1} →
  {G : Type u_2} →
    [inst : SMul G X] →
      {motive : Equidecomp X G → Sort u} →
        (t : Equidecomp X G) →
          ((toPartialEquiv : PartialEquiv X X) →
              (isDecompOn' : ∃ S, Equidecomp.IsDecompOn (↑toPartialEquiv) toPartialEquiv.source S) →
                motive { toPartialEquiv := toPartialEquiv, isDecompOn' := isDecompOn' }) →
            motive t