let L be non empty satisfying_DN_1 ComplLLattStr ; :: thesis: for x, y being Element of L holds ((x + y) `) + ((y + (y `)) `) = (x + y) `
let x, y be Element of L; :: thesis: ((x + y) `) + ((y + (y `)) `) = (x + y) `
set X = (x + y) ` ;
set Y = y ` ;
((x + y) `) + (((((y `) + ((x + y) `)) `) + (y `)) `) = (x + y) ` by Th28;
hence ((x + y) `) + ((y + (y `)) `) = (x + y) ` by Th18; :: thesis: verum