let K be non empty right_complementable Abelian add-associative right_zeroed well-unital distributive associative doubleLoopStr ; :: thesis: for V being VectSp of K
for v being Vector of V
for W1, W2 being Subspace of V ex v1, v2 being Vector of V st v |-- (W1,W2) = [v1,v2]
let V be VectSp of K; :: thesis: for v being Vector of V
for W1, W2 being Subspace of V ex v1, v2 being Vector of V st v |-- (W1,W2) = [v1,v2]
let v be Vector of V; :: thesis: for W1, W2 being Subspace of V ex v1, v2 being Vector of V st v |-- (W1,W2) = [v1,v2]
let W1, W2 be Subspace of V; :: thesis: ex v1, v2 being Vector of V st v |-- (W1,W2) = [v1,v2]
take (v |-- (W1,W2)) `1 ; :: thesis: ex v2 being Vector of V st v |-- (W1,W2) = [((v |-- (W1,W2)) `1),v2]
take (v |-- (W1,W2)) `2 ; :: thesis: v |-- (W1,W2) = [((v |-- (W1,W2)) `1),((v |-- (W1,W2)) `2)]
thus v |-- (W1,W2) = [((v |-- (W1,W2)) `1),((v |-- (W1,W2)) `2)] by MCART_1:21; :: thesis: verum