let L be non empty satisfying_DN_1 ComplLLattStr ; :: thesis: for x, y being Element of L holds (((x + y) `) + (((x `) + y) `)) ` = y
let x, y be Element of L; :: thesis: (((x + y) `) + (((x `) + y) `)) ` = y
set Z = (x + (x `)) ` ;
(((x + y) `) + ((((((x + (x `)) `) + x) `) + y) `)) ` = y by Th5;
hence (((x + y) `) + (((x `) + y) `)) ` = y by Th3; :: thesis: verum