let V be RealLinearSpace; :: thesis: for W1, W2 being Subspace of V holds the carrier of (W1 /\ W2) c= the carrier of (W1 + W2)

let W1, W2 be Subspace of V; :: thesis: the carrier of (W1 /\ W2) c= the carrier of (W1 + W2)

( the carrier of (W1 /\ W2) c= the carrier of W1 & the carrier of W1 c= the carrier of (W1 + W2) ) by Lm2, Lm4;

hence the carrier of (W1 /\ W2) c= the carrier of (W1 + W2) ; :: thesis: verum

let W1, W2 be Subspace of V; :: thesis: the carrier of (W1 /\ W2) c= the carrier of (W1 + W2)

( the carrier of (W1 /\ W2) c= the carrier of W1 & the carrier of W1 c= the carrier of (W1 + W2) ) by Lm2, Lm4;

hence the carrier of (W1 /\ W2) c= the carrier of (W1 + W2) ; :: thesis: verum