∀ {n : Type u_2} {R : Type u_3} [inst : Ring R] [inst_1 : PartialOrder R] [inst_2 : StarRing R] [inst_3 : Fintype n]
  [inst_4 : DecidableEq n] {U x : Matrix n n R}, IsUnit U → ((U * x * star U).PosSemidef ↔ x.PosSemidef)