reserve X for set;
reserve a,b,c,k,m,n for Nat;
reserve i,j for Integer;
reserve r,s for Real;
reserve p,p1,p2,p3 for Prime;

theorem Th13:
  for b being finite-support Function holds
  dom(b*canFS(support b)) = dom canFS(support b)
  proof
    let b be finite-support Function;
A1: rng canFS(support b) c= support b by FINSEQ_1:def 4;
    support b c= dom b by PRE_POLY:37;
    then rng canFS(support b) c= dom b by A1;
    hence thesis by RELAT_1:27;
  end;
