let F be Field; for V being VectSp of F
for W being Subspace of V
for L being Linear_Compl of W
for v being Element of V holds
( (v |-- (W,L)) `1 in W & (v |-- (W,L)) `2 in L )
let V be VectSp of F; for W being Subspace of V
for L being Linear_Compl of W
for v being Element of V holds
( (v |-- (W,L)) `1 in W & (v |-- (W,L)) `2 in L )
let W be Subspace of V; for L being Linear_Compl of W
for v being Element of V holds
( (v |-- (W,L)) `1 in W & (v |-- (W,L)) `2 in L )
let L be Linear_Compl of W; for v being Element of V holds
( (v |-- (W,L)) `1 in W & (v |-- (W,L)) `2 in L )
let v be Element of V; ( (v |-- (W,L)) `1 in W & (v |-- (W,L)) `2 in L )
V is_the_direct_sum_of W,L
by Th38;
hence
( (v |-- (W,L)) `1 in W & (v |-- (W,L)) `2 in L )
by Def6; verum