Proposition. for all integers x, y, and z, if x|y and y z, then x|z proof. let a, b, and c be arbitrary integers. suppose that alb and b|c. since a|b, there is an integer whose product with a is b. let n be such an integer, so a xn = b. since bc, there is an integer whose product with b is c. let m be such an integer, so integer bxm 3 с. тhus, c 3d b x m %3 (а х п) х т %3d ах (n m). since n x m is an a c. since a, b, and c were arbitrary, we have an integer whose product with a is c, so we have proved the proposition in the video, we gave a partial natural deduction formalization of this proof. give a full formalization, yourself to the assumption vavyvz (xx y) x z xx (yxz)