let L be non empty satisfying_DN_1 ComplLattStr ; :: thesis: for x, y being Element of L holds (x + ((x + (y ` )) ` )) ` = (x + y) `
let x, y be Element of L; :: thesis: (x + ((x + (y ` )) ` )) ` = (x + y) `
(x + ((((x + y) ` ) + x) ` )) ` = (x + y) ` by Th8;
hence (x + ((x + (y ` )) ` )) ` = (x + y) ` by Th44; :: thesis: verum