∀ {X : Type u} {isSemilatticeSup : SemilatticeSup X} {isOrderBot : OrderBot X} {X_1 : Type u}
  {isSemilatticeSup_1 : SemilatticeSup X_1} {isOrderBot_1 : OrderBot X_1},
  { X := X, isSemilatticeSup := isSemilatticeSup, isOrderBot := isOrderBot } =
      { X := X_1, isSemilatticeSup := isSemilatticeSup_1, isOrderBot := isOrderBot_1 } →
    X = X_1 ∧ isSemilatticeSup ≍ isSemilatticeSup_1 ∧ isOrderBot ≍ isOrderBot_1