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
( V is_the_direct_sum_of L,W & V is_the_direct_sum_of W,L )
let V be VectSp of F; :: thesis: for W being Subspace of V
for L being Linear_Compl of W holds
( V is_the_direct_sum_of L,W & V is_the_direct_sum_of W,L )
let W be Subspace of V; :: thesis: for L being Linear_Compl of W holds
( V is_the_direct_sum_of L,W & V is_the_direct_sum_of W,L )
let L be Linear_Compl of W; :: thesis: ( V is_the_direct_sum_of L,W & V is_the_direct_sum_of W,L )
thus V is_the_direct_sum_of L,W by Def5; :: thesis: V is_the_direct_sum_of W,L
hence V is_the_direct_sum_of W,L by Lm17; :: thesis: verum