∀ (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)