let L be non empty satisfying_DN_1 ComplLLattStr ; :: thesis: for x, y being Element of L holds (x + ((((x + y) `) + x) `)) ` = (x + y) `
let x, y be Element of L; :: thesis: (x + ((((x + y) `) + x) `)) ` = (x + y) `
set X = (x + y) ` ;
set Y = x;
(((((((x + y) `) + x) `) + ((x + y) `)) `) + ((((x + y) `) + x) `)) ` = (x + y) ` by Th7;
hence (x + ((((x + y) `) + x) `)) ` = (x + y) ` by Th7; :: thesis: verum