let GF be Ring; :: thesis: for V being LeftMod of GF
for A, B being Subset of V holds Lin (A /\ B) is Subspace of (Lin A) /\ (Lin B)
let V be LeftMod of GF; :: thesis: for A, B being Subset of V holds Lin (A /\ B) is Subspace of (Lin A) /\ (Lin B)
let A, B be Subset of V; :: thesis: Lin (A /\ B) is Subspace of (Lin A) /\ (Lin B)
( Lin (A /\ B) is Subspace of Lin A & Lin (A /\ B) is Subspace of Lin B ) by Th13, XBOOLE_1:17;
hence Lin (A /\ B) is Subspace of (Lin A) /\ (Lin B) by VECTSP_5:19; :: thesis: verum