let L be non empty satisfying_DN_1 ComplLLattStr ; :: thesis: for x, y, z being Element of L holds ((((x + y) ` ) + ((((x + y) ` ) + ((x + z) ` )) ` )) ` ) + y = y
let x, y, z be Element of L; :: thesis: ((((x + y) ` ) + ((((x + y) ` ) + ((x + z) ` )) ` )) ` ) + y = y
set Y = (((x + y) ` ) + ((x + z) ` )) ` ;
((((y + ((((x + y) ` ) + ((x + z) ` )) ` )) ` ) + ((((x + y) ` ) + ((x + z) ` )) ` )) ` ) + y = y by Th28;
hence ((((x + y) ` ) + ((((x + y) ` ) + ((x + z) ` )) ` )) ` ) + y = y by Th37; :: thesis: verum