let V be RealLinearSpace; :: thesis: rng (ZeroLC V) c= INT
let y be object ; :: according to TARSKI:def 3 :: thesis: ( not y in rng (ZeroLC V) or y in INT )
assume A1: y in rng (ZeroLC V) ; :: thesis: y in INT
consider x being object such that
A2: ( x in the carrier of V & y = (ZeroLC V) . x ) by A1, FUNCT_2:11;
reconsider z = x as VECTOR of V by A2;
(ZeroLC V) . z = 0 by RLVECT_2:20;
hence y in INT by A2, NUMBERS:17; :: thesis: verum