let L be non empty satisfying_DN_1 ComplLLattStr ; :: thesis: for x, y being Element of L holds (((((x + y) ` ) + x) ` ) + ((x + y) ` )) ` = x
let x, y be Element of L; :: thesis: (((((x + y) ` ) + x) ` ) + ((x + y) ` )) ` = x
set X = (x + y) ` ;
(((((x + y) ` ) + x) ` ) + ((((x + ((x + y) ` )) ` ) + ((((((x + (x ` )) ` ) + x) ` ) + ((x + y) ` )) ` )) ` )) ` = x by Th4;
hence (((((x + y) ` ) + x) ` ) + ((x + y) ` )) ` = x by Th5; :: thesis: verum