let L be non empty satisfying_DN_1 ComplLLattStr ; :: thesis: for x, y, z, u being Element of L holds (((x + y) ` ) + ((((z + x) ` ) + ((((((y + (y ` )) ` ) + y) ` ) + ((y + u) ` )) ` )) ` )) ` = y
let x, y, z, u be Element of L; :: thesis: (((x + y) ` ) + ((((z + x) ` ) + ((((((y + (y ` )) ` ) + y) ` ) + ((y + u) ` )) ` )) ` )) ` = y
(((y + (y ` )) ` ) + y) ` = y ` by Th3;
hence (((x + y) ` ) + ((((z + x) ` ) + ((((((y + (y ` )) ` ) + y) ` ) + ((y + u) ` )) ` )) ` )) ` = y by Th2; :: thesis: verum