let L be non empty satisfying_DN_1 ComplLLattStr ; :: thesis: for x, y, z, u being Element of L holds (((x + y) ` ) + ((((z + x) ` ) + (((y ` ) + ((y + u) ` )) ` )) ` )) ` = y
let x, y, z, u be Element of L; :: thesis: (((x + y) ` ) + ((((z + x) ` ) + (((y ` ) + ((y + u) ` )) ` )) ` )) ` = y
consider v being Element of L;
(((x + z) ` ) + ((((((y + u) ` ) + x) ` ) + (((z ` ) + ((z + v) ` )) ` )) ` )) ` = z by Th1;
hence (((x + y) ` ) + ((((z + x) ` ) + (((y ` ) + ((y + u) ` )) ` )) ` )) ` = y by Th1; :: thesis: verum