let L be non empty satisfying_DN_1 ComplLLattStr ; :: thesis: for x, y being Element of L holds (((((x + y) `) + x) `) + y) ` = (y + y) `
let x, y be Element of L; :: thesis: (((((x + y) `) + x) `) + y) ` = (y + y) `
set X = (x + y) ` ;
(((x + y) `) + ((((((x + y) `) + x) `) + y) `)) ` = y by Th5;
hence (((((x + y) `) + x) `) + y) ` = (y + y) ` by Th16; :: thesis: verum