reserve a,b,c,k,m,n for Nat;
reserve i,j,x,y for Integer;
reserve p,q for Prime;
reserve r,s for Real;

theorem Th28:
  n > 0 implies p < primenumber(n+primeindex p)
  proof
    assume
A1: n > 0;
A2: p = primenumber primeindex p by Def4;
    assume p >= primenumber(n+primeindex p);
    then 0+primeindex p >= n+primeindex p by A2,MOEBIUS2:21;
    hence thesis by A1,XREAL_1:6;
  end;
