Mathematics, 30.08.2019 22:30 AlexBeWare1210
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 Ρ. Ρhus, c 3d b x m %3 (Π° Ρ ΠΏ) Ρ Ρ %3d Π°Ρ (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)
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Proposition. for all integers x, y, and z, if x|y and y z, then x|z proof. let a, b, and c be arbitr...