let L be non empty satisfying_DN_1 ComplLattStr ; :: thesis: for x, y, z being Element of L holds ((((((x + y) ` ) + z) ` ) + (((x ` ) + y) ` )) ` ) + y = (x ` ) + y
let x, y, z be Element of L; :: thesis: ((((((x + y) ` ) + z) ` ) + (((x ` ) + y) ` )) ` ) + y = (x ` ) + y
((((((x + y) ` ) + z) ` ) + (((x ` ) + y) ` )) ` ) + y = (((x ` ) + y) ` ) ` by Th47;
hence ((((((x + y) ` ) + z) ` ) + (((x ` ) + y) ` )) ` ) + y = (x ` ) + y by Th23; :: thesis: verum