let V be Z_Module; :: thesis: for W being with_Linear_Compl Submodule of V
for L being Linear_Compl of W holds W is Linear_Compl of L
let W be with_Linear_Compl Submodule of V; :: thesis: for L being Linear_Compl of W holds W is Linear_Compl of L
let L be Linear_Compl of W; :: thesis: W is Linear_Compl of L
V is_the_direct_sum_of L,W by Def19;
then A1: V is_the_direct_sum_of W,L by VECTSP_5:41;
then L is with_Linear_Compl ;
hence W is Linear_Compl of L by Def19, A1; :: thesis: verum