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 <%z0,(1. L)%>,x = z0 + x
let z0, z1, x be Element of L; :: thesis: eval <%z0,(1. L)%>,x = z0 + x
thus eval <%z0,(1. L)%>,x = z0 + ((1. L) * x) by Th45
.= z0 + x by VECTSP_1:def 16 ; :: thesis: verum