let V be RealLinearSpace; :: 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_1:23; :: thesis: verum