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 Th39:
  for P,R being Relation st rng R c= rng P & P is positive-yielding holds
  R is positive-yielding
  proof
    let P,R be Relation;
    assume
A1: rng R c= rng P & P is positive-yielding;
    let r be Real;
    thus thesis by A1,PARTFUN3:def 1;
  end;
