let X be RealNormSpace; :: thesis: for A being Subset of X holds
( A is closed iff Cl A = A )
let A be Subset of X; :: thesis: ( A is closed iff Cl A = A )
reconsider A1 = A as Subset of (LinearTopSpaceNorm X) by NORMSP_2:def 4;
A1: Cl A1 = Cl A by EQCL1;
( A1 is closed iff A is closed ) by NORMSP_2:32;
hence ( A is closed iff Cl A = A ) by A1, PRE_TOPC:22; :: thesis: verum