let L be non empty right_complementable add-associative right_zeroed left-distributive well-unital doubleLoopStr ; :: thesis: for z0, z1, x being Element of L holds eval (<%(0. L),(1. L)%>,x) = x
let z0, z1, x be Element of L; :: thesis: eval (<%(0. L),(1. L)%>,x) = x
thus eval (<%(0. L),(1. L)%>,x) = (0. L) + ((1. L) * x) by Th44
.= (0. L) + x
.= x by RLVECT_1:4 ; :: thesis: verum