let L be non empty satisfying_DN_1 ComplLLattStr ; :: thesis: for x, y being Element of L holds ((((x + (y `)) `) `) + y) ` = ((y `) + y) `
let x, y be Element of L; :: thesis: ((((x + (y `)) `) `) + y) ` = ((y `) + y) `
set Y = y ` ;
set Z = y;
(((((x + (y `)) `) + (((y `) + y) `)) `) + y) ` = ((y `) + y) ` by Th15;
hence ((((x + (y `)) `) `) + y) ` = ((y `) + y) ` by Th31; :: thesis: verum