let L be non empty satisfying_DN_1 ComplLattStr ; :: thesis: for x, y, z, u being Element of L holds (((x + y) ` ) + ((((z + x) ` ) + (((y ` ) + ((u + y) ` )) ` )) ` )) ` = y
let x, y, z, u be Element of L; :: thesis: (((x + y) ` ) + ((((z + x) ` ) + (((y ` ) + ((u + y) ` )) ` )) ` )) ` = y
set U = (((u + z) ` ) + ((u + y) ` )) ` ;
(((x + y) ` ) + ((((z + x) ` ) + (((y ` ) + ((y + ((((u + z) ` ) + ((u + y) ` )) ` )) ` )) ` )) ` )) ` = y by Th2;
hence (((x + y) ` ) + ((((z + x) ` ) + (((y ` ) + ((u + y) ` )) ` )) ` )) ` = y by Th10; :: thesis: verum