let F be Field; :: thesis: for V being VectSp of F
for W being Subspace of V
for L being Linear_Compl of W holds
( W /\ L = (0). V & L /\ W = (0). V )
let V be VectSp of F; :: thesis: for W being Subspace of V
for L being Linear_Compl of W holds
( W /\ L = (0). V & L /\ W = (0). V )
let W be Subspace of V; :: thesis: for L being Linear_Compl of W holds
( W /\ L = (0). V & L /\ W = (0). V )
let L be Linear_Compl of W; :: thesis: ( W /\ L = (0). V & L /\ W = (0). V )
A1: V is_the_direct_sum_of W,L by Th38;
hence W /\ L = (0). V ; :: thesis: L /\ W = (0). V
thus L /\ W = (0). V by A1; :: thesis: verum