let L be non empty satisfying_DN_1 ComplLLattStr ; :: 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 Th11;
hence ((((((x + y) ` ) + z) ` ) + (((x ` ) + y) ` )) ` ) + y = (((x ` ) + y) ` ) ` by Th23; :: thesis: verum