let V be Z_Module; :: thesis: for A, B being Subset of V holds Lin (A /\ B) is Submodule of (Lin A) /\ (Lin B)
let A, B be Subset of V; :: thesis: Lin (A /\ B) is Submodule of (Lin A) /\ (Lin B)
( Lin (A /\ B) is Submodule of Lin A & Lin (A /\ B) is Submodule of Lin B ) by Th70, XBOOLE_1:17;
hence Lin (A /\ B) is Submodule of (Lin A) /\ (Lin B) by Lm3; :: thesis: verum