set Q = the non-empty MSAlgebra over J;

set s = the sort-preserving Function of [:(Union the Sorts of the non-empty MSAlgebra over J),(Union [|X, the Sorts of the non-empty MSAlgebra over J|]):],(Union the Sorts of the non-empty MSAlgebra over J);

take K = SubstMSAlgebra(# the Sorts of the non-empty MSAlgebra over J, the Charact of the non-empty MSAlgebra over J, the sort-preserving Function of [:(Union the Sorts of the non-empty MSAlgebra over J),(Union [|X, the Sorts of the non-empty MSAlgebra over J|]):],(Union the Sorts of the non-empty MSAlgebra over J) #); :: thesis: K is non-empty

thus the Sorts of K is V2() ; :: according to MSUALG_1:def 3 :: thesis: verum

set s = the sort-preserving Function of [:(Union the Sorts of the non-empty MSAlgebra over J),(Union [|X, the Sorts of the non-empty MSAlgebra over J|]):],(Union the Sorts of the non-empty MSAlgebra over J);

take K = SubstMSAlgebra(# the Sorts of the non-empty MSAlgebra over J, the Charact of the non-empty MSAlgebra over J, the sort-preserving Function of [:(Union the Sorts of the non-empty MSAlgebra over J),(Union [|X, the Sorts of the non-empty MSAlgebra over J|]):],(Union the Sorts of the non-empty MSAlgebra over J) #); :: thesis: K is non-empty

thus the Sorts of K is V2() ; :: according to MSUALG_1:def 3 :: thesis: verum