let s be SynTypes_Calculus; :: thesis: for x, z, y being type of s holds
( <*> the carrier of s ==>. ((x /" z) /" (y /" z)) /" (x /" y) & <*> the carrier of s ==>. (y \ x) \ ((z \ y) \ (z \ x)) )
let x, z, y be type of s; :: thesis: ( <*> the carrier of s ==>. ((x /" z) /" (y /" z)) /" (x /" y) & <*> the carrier of s ==>. (y \ x) \ ((z \ y) \ (z \ x)) )
( <*(x /" y)*> ==>. (x /" z) /" (y /" z) & <*(y \ x)*> ==>. (z \ y) \ (z \ x) ) by Th14, Th15;
hence ( <*> the carrier of s ==>. ((x /" z) /" (y /" z)) /" (x /" y) & <*> the carrier of s ==>. (y \ x) \ ((z \ y) \ (z \ x)) ) by Th19; :: thesis: verum