let F be Field; :: thesis: 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; :: thesis: 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; :: thesis: 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; :: thesis: 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; :: thesis: ( (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; :: thesis: verum