let L be non empty right_complementable right-distributive add-associative right_zeroed doubleLoopStr ; :: thesis: ( L is domRing-like implies L is almost_left_cancelable )
assume A1: L is domRing-like ; :: thesis: L is almost_left_cancelable
let x be Element of L; :: according to ALGSTR_0:def 35 :: thesis: ( x = 0. L or x is left_mult-cancelable )
assume A2: x <> 0. L ; :: thesis: x is left_mult-cancelable
let y, z be Element of L; :: according to ALGSTR_0:def 20 :: thesis: ( not x * y = x * z or y = z )
assume x * y = x * z ; :: thesis: y = z
then (x * y) - (x * z) = 0. L by RLVECT_1:15;
then x * (y - z) = 0. L by VECTSP_1:11;
then y - z = 0. L by A2, A1;
hence y = z by RLVECT_1:21; :: thesis: verum