let L be non empty satisfying_Sh_1 ShefferStr ; :: thesis: for x, y being Element of L holds ((x | y) | (((x | y) | (x | y)) | (x | y))) | ((x | y) | (x | y)) = y | ((((x | y) | (x | y)) | y) | y)

let x, y be Element of L; :: thesis: ((x | y) | (((x | y) | (x | y)) | (x | y))) | ((x | y) | (x | y)) = y | ((((x | y) | (x | y)) | y) | y)

(y | ((((x | y) | (x | y)) | y) | y)) | (x | y) = (x | y) | (x | y) by Th8;

hence ((x | y) | (((x | y) | (x | y)) | (x | y))) | ((x | y) | (x | y)) = y | ((((x | y) | (x | y)) | y) | y) by Th2; :: thesis: verum

let x, y be Element of L; :: thesis: ((x | y) | (((x | y) | (x | y)) | (x | y))) | ((x | y) | (x | y)) = y | ((((x | y) | (x | y)) | y) | y)

(y | ((((x | y) | (x | y)) | y) | y)) | (x | y) = (x | y) | (x | y) by Th8;

hence ((x | y) | (((x | y) | (x | y)) | (x | y))) | ((x | y) | (x | y)) = y | ((((x | y) | (x | y)) | y) | y) by Th2; :: thesis: verum